<PAGE>   1

                                                                     EXHIBIT 4.4


         THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED WITH THE
         SECURITIES AND EXCHANGE COMMISSION IN RELIANCE UPON AN EXEMPTION FROM
         REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"),
         AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN
         EFFECTIVE REGISTRATION STATEMENT UNDER THE ACT OR PURSUANT TO AN
         AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE
         REGISTRATION REQUIREMENTS OF THE ACT.


June 29, 2000                                                  Right to Purchase
                                                                  834,836 Shares
                                                                of Common Stock,
                                                                par value $0.001
                                                                       per share

                                GERON CORPORATION
                             STOCK PURCHASE WARRANT

Registered Owner:

         This warrant is a duly authorized warrant (the "Warrant") of Geron
Corporation, a Delaware corporation (the "Company") referred to in the
Securities Purchase Agreement (the "Purchase Agreement") dated as of June 29,
2000 by and between the Company and the Purchaser (as defined in the Purchase
Agreement). This Warrant is subject to the terms and conditions of the Purchase
Agreement, a copy of which is on file at and may be obtained from the Company at
its principal office at the address set forth in Section 11 hereof. This
certifies that, for value received the Company grants the following rights to
the Registered Owner, or assigns, of this Warrant:

         1. ISSUE. Upon tender (as defined in section 5 hereof) to the Company,
the Company shall issue to the Registered Owner, RGC International Investors,
LDC, or assigns, up to the number of shares specified in paragraph 2 hereof of
fully paid and non-assessable shares of Common Stock, par value $.001 per share
("Common Stock"), that the Registered Owner, or assigns, is otherwise entitled
to purchase.

         2. NUMBER OF SHARES. The total number of shares of Common Stock that
the Registered Owner, or assigns, of this Warrant is entitled to receive upon
exercise of this Warrant is 834,836 shares of common Stock, subject to
adjustment from time to time as set forth in paragraph 6 below. The Company
shall at all times have authorized, reserved and held available sufficient
shares of Common Stock to satisfy all conversion and purchase rights represented
by outstanding convertible securities, options and warrants, including this
Warrant, for issuance upon exercise of this Warrant, such number of shares equal
to 125% of the shares for which it may then be exercised. The Company covenants
and agrees that all shares of Common Stock that may be issued upon the exercise
of this Warrant shall, upon issuance, be duly and validly issued, fully paid and
non-assessable, and free from all taxes, liens and charges with respect to the
purchase and the issuance of the shares.

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         3. EXERCISE PRICE. The initial exercise price of this Warrant, the
price at which the shares of stock issuable upon exercise of this Warrant may be
purchased, is $37.43 and subject to adjustment from time to time pursuant to the
provisions of paragraph 6 below (the "Exercise Price").

         3A. PAYMENT OF EXERCISE PRICE. The Registered Owner may pay the
Exercise Price in one of the following manners:

                  (i) Cash Exercise. The Registered Owner shall deliver
immediately available funds or a check payable to the Company; or

                  (ii) Cashless Exercise. At such time as, but only at such time
as, after the 120th day after the date of issuance of this Warrant, all of the
Registerable Securities (as defined in the Registration Rights Agreement) are
not registered pursuant to an effective registration statement, the Registered
Owner shall have the right to surrender this Warrant to the Company together
with a notice of cashless exercise, in which event the Company shall issue to
the Registered Owner the number of Warrant Shares determined as follows:

         where: X = Y (A-B)/A

                X = the number of Warrant Shares (as defined in the
                Purchase Agreement) to be issued to the Registered Owner

                Y = the number of Warrant Shares with
                respect to which this Warrant is being
                exercised

                A = the average of the Per Share Market
                Value of the Common Stock for the five (5)
                Trading Days immediately prior to (but not
                including) the date of exercise

                B = the Exercise Price

For purposes of Rule 144 promulgated under the Securities Act, it is intended,
understood and acknowledged that the Warrant Shares issued in a cashless
exercise transaction shall be deemed to have been acquired by the Registered
Owner, and the holding period for the Warrant Shares shall be deemed to have
been commenced, on the issue date to the extent permitted by Rule 144.

         4. EXERCISE PERIOD. This Warrant may be exercised at any time and from
time to time during the period beginning on June 29, 2000 (the "Issue Date") and
up to and including the date which is 540 days after the Issue Date (the
"Exercise Period"). If not exercised during this period, this Warrant and all
rights granted under this Warrant shall expire and lapse.


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<PAGE>   3

         5. TENDER. This Warrant may be exercised, in whole or in part, by
actual delivery of (i) the Exercise Price in cash, (ii) a duly executed Warrant
Exercise Form, a copy of which is attached to this Warrant as Exhibit A,
properly executed by the Registered Owner, or assigns, of this Warrant, and
(iii) by surrender of This Warrant. The payment and Warrant Exercise Form must
be delivered, personally or by mail, to the registered office of the Company.
Documents sent by mail shall be deemed to be delivered when they are received by
the Company. If this Warrant shall have been exercised only in part, then,
unless this Warrant has expired, the Company shall, at its expense, at the time
of delivery of such certificates, deliver to the holder a new Warrant
representing the number of shares with respect to which this Warrant shall not
then have been exercised.

         6. ADJUSTMENT OF EXERCISE PRICE.

                  (a) Common Stock Dividends; Common Stock Splits; Reverse
Common Stock Splits. If the Company, at any time while this Warrant is
outstanding, (a) shall pay a stock dividend on its Common Stock, (b) subdivide
outstanding shares of Common Stock into a larger number of shares, (c) combine
outstanding shares of Common Stock into a smaller number of shares, or (d) issue
by reclassification of shares of Common Stock any shares of capital stock of the
Company, the Exercise Price shall be multiplied by a fraction the numerator of
which shall be the number of shares of Common Stock (excluding treasury shares,
if any) outstanding before such event and the denominator of which shall be the
number of shares of Common Stock outstanding after such event. Any adjustment
made pursuant to this paragraph (6)(a) shall become effective immediately after
the record date for the determination of shareholders entitled to receive such
dividend or distribution and shall become effective immediately after the
effective date in the case of a subdivision, combination or re-classification.

                  (b) Rights; Options; Warrants. If the Company, during the
period commencing on the Closing Date (as defined in the Purchase Agreement)
through and including the date which is 12 months from the Issue Date, shall
issue rights or warrants to all of the holders of Common Stock entitling them to
subscribe for or purchase shares of Common Stock at a price per share less than
$26.95, the Exercise Price shall be multiplied by a fraction, the denominator of
which shall be the number of shares of Common Stock (excluding treasury shares,
if any) outstanding on the date of issuance of such rights or warrants plus the
number of additional shares of Common Stock offered for subscription or
purchase, and the numerator of which shall be the number of shares of Common
Stock (excluding treasury shares, if any) outstanding on the date of issuance of
such rights or warrants plus the number of shares which the aggregate offering
price of the total number of shares so offered would purchase at $26.95 per
share. Such adjustment shall be made whenever such rights or warrants are
issued, and shall become effective immediately after the record date for the
determination of shareholders entitled to receive such rights or warrants.
However, upon the expiration of any right or warrant to purchase Common Stock
the issuance of which resulted in an adjustment in the Exercise Price pursuant
to this paragraph (6)(b), if any such right or warrant shall expire and all or
any portion thereof shall not have been exercised, the Exercise Price shall
immediately upon such expiration be re-computed and effective immediately upon
such expiration be increased to the price which it would have been (but
reflecting any other adjustments in the Exercise Price made pursuant to the
provisions of Section 6(g) after the issuance of such rights or warrants) had
the adjustment of the Exercise Price made upon the issuance of such rights or
warrants been made on the basis of offering for subscription or purchase only
that number of shares of


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<PAGE>   4

Common Stock (if any) actually purchased upon the exercise of such rights or
warrants actually exercised; provided, however, that if (X) (1) the Registration
Statement (as defined in the Registration Rights Agreement) is then in effect
and has been in effect and sales of all of the Registrable Securities (as
defined in the Registration Rights Agreement) can be made thereunder for at
least twenty (20) Trading Days prior to a Trigger Date (as defined below); (2)
the Company has, at all times prior to the Trigger Date, a sufficient number of
authorized shares of Common Stock reserved for issuance upon full conversion of
all of the Securities (as defined in the Purchase Agreement) issued pursuant to
the Purchase Agreement; and (3) no Event of Default shall have occurred and be
continuing on the Trigger Date or at any time during the twenty (20) Trading
Days prior to a Trigger Date; and (Y) the Per Share Market Value is greater than
150% of the Conversion Price (as defined in the debentures issued pursuant to
the Purchase Agreement (the "Debentures")) in effect on the Closing Date (as
defined in the Purchase Agreement) for any five (5) consecutive Trading Days
prior to the 180th day following the Issue Date (the last day of such five (5)
consecutive Trading Day period being referred to herein as the "Trigger Date"),
then this provision shall expire automatically on the 180th day following the
Issue Date.

                  (c) Subscription Rights. If the Company, during the period
commencing on the Closing Date (as defined in the Purchase Agreement) through
and including the date which is 12 months from the Issue Date, shall distribute
to all of the holders of Common Stock evidences of its indebtedness or assets or
rights or warrants to subscribe for or purchase any security (excluding those
referred to in paragraphs 6(a) and (b) above), then in each such case the
Exercise Price at which the Warrant shall thereafter be exercisable shall be
determined by multiplying the Exercise Price in effect immediately prior to the
record date fixed for determination of shareholders entitled to receive such
distribution by a fraction the denominator of which shall be the Per Share
Market Value of Common Stock determined as of the record date mentioned above,
and the numerator of which shall be such Per Share Market Value of the Common
Stock on such record date less the then fair market value at such record date of
the portion of such assets or evidence of indebtedness so distributed applicable
to one outstanding share of Common Stock as determined by the Board of Directors
in good faith; provided, however, that in the event of a distribution exceeding
ten percent (10%) of the net assets of the Company, such fair market value shall
be determined by a nationally recognized or major regional investment banking
firm or firm of independent certified public accountants of recognized standing
(an "Appraiser") selected in good faith by the Registered Owner of the Warrant;
and provided, further, that the Company, after receipt of the determination by
such Appraiser shall have the right to select an additional Appraiser meeting
the same qualifications, in good faith, in which case the fair market value
shall be equal to the average of the determinations by each such Appraiser. Such
adjustment shall be made whenever any such distribution is made and shall become
effective immediately after the record date mentioned above; provided, however,
that if (X) (1) the Registration Statement (as defined in the Registration
Rights Agreement) is then in effect and has been in effect and sales of all of
the Registrable Securities (as defined in the Registration Rights Agreement) can
be made thereunder for at least twenty (20) Trading Days prior to a Trigger
Date; (2) the Company has, at all times prior to the Trigger Date, a sufficient
number of authorized shares of Common Stock reserved for issuance upon full
conversion of all of the Securities (as defined in the Purchase Agreement)
issued pursuant to the Purchase Agreement; and (3) no Event of Default shall
have occurred and be continuing on the Trigger Date or at any time during the
twenty (20) Trading Days prior to a Trigger Date; and (Y) the Per Share Market
Value is greater than 150% of the Conversion Price (as defined in the
Debentures) in effect on the Closing Date (as defined in the


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<PAGE>   5

Purchase Agreement) for any five (5) consecutive Trading Days prior to the 180th
day following the Issue Date, then this provision shall expire automatically on
the 180th day following the Issue Date.

                  (d) Rounding. All calculations under this section 6 shall be
made to the nearest cent or the nearest l/l00th of a share, as the case may be.

                  (e) Notice of Adjustment. Whenever the Exercise Price is
adjusted pursuant to paragraphs 6(a), (b), (c) or (h), the Company shall
promptly mail to the holder of the Warrant, a notice setting forth the Exercise
Price after such adjustment and setting forth a brief statement of the facts
requiring such adjustment. Upon each adjustment of the Exercise Price pursuant
paragraphs 6(a), (b), (c) or (h), the number of shares of Common Stock issuable
upon exercise of this Warrant shall be adjusted by multiplying a number equal to
the Exercise Price in effect immediately prior to such adjustment by the number
of shares of Common Stock issuable upon exercise of this Warrant immediately
prior to such adjustment and dividing the product so obtained by the adjusted
Exercise Price.

                  (f) Redemption Events. In case of (A) any reclassification of
the Common Stock, (B) any consolidation or merger of the Company with or into
another person pursuant to which (i) a majority of the Company's Board of
Directors will not constitute a majority of the board of directors of the
surviving entity or (ii) less than 51% of the outstanding shares of the capital
stock of the surviving entity will be held by the same shareholders of the
Company prior to such reclassification, consolidation or merger, (C) the sale or
transfer of all or substantially all of the assets of the Company, (D) any
compulsory share exchange pursuant to which the Common Stock is converted into
other securities, cash or property, (E) suspension from listing or delisting of
the Common Stock from the National Market System of the Nasdaq Stock Market
("Nasdaq") or any other exchange on which the Common Stock is listed for a
period of five (5) consecutive Trading Days, (F) the Company's notice to any
Registered Owner, including by way of public announcement, at any time, of its
intention, for any reason, not to comply with proper requests for the exercise
of any such warrants, or (G) a breach by the Company of any representation,
warranty, covenant or other term or condition of the Purchase Agreement, the
Registration Rights Agreement or any other agreement, document, certificate or
other instrument delivered in connection with the transactions contemplated
thereby or hereby, except to the extent that such breach would not have a
Material Adverse Effect (as defined in Section 3(a) of the Purchase Agreement)
and except, in the case of a breach of a covenant which is curable, only if such
breach continues for a period of at least ten (10) days after the Company knows
or reasonably should have known of the existence of such breach (clauses (A)
through (G) above referred to as a "Redemption Event"), the holder of the
Warrant shall have the right thereafter to exercise the Warrant within ten (10)
Business Days of the Redemption Event for the shares of stock and other
securities, cash and property receivable upon or deemed to be held by holders of
Common Stock following such Redemption Event, and the holder of the Warrant
shall be entitled upon such event to receive such amount of securities, cash or
property as the shares of the Common Stock of the Company into which the Warrant
could have been converted immediately prior to such Redemption Event would have
been entitled.


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<PAGE>   6

         (g) Reclassification, Etc. If:

                  A. the Company shall declare a dividend (or any other
         distribution) on its Common Stock; or

                  B. the Company shall declare a special nonrecurring cash
         dividend on or a redemption of its Common Stock; or

                  C. the Company shall authorize the granting to all of the
         holders of the Common Stock rights or warrants to subscribe for or
         purchase any shares of capital stock of any class or of any rights; or

                  D. the approval of any shareholders of the Company shall be
         required in connection with any reclassification of the Common Stock of
         the Company, any consolidation or merger to which the Company is a
         party, any sale or transfer of all or substantially all of the assets
         of the Company, of any compulsory share exchange whereby the Common
         Stock is converted into other securities, cash or property; or

                  E. the Company shall authorize the voluntary or involuntary
         dissolution, liquidation or winding up of the affairs of the Company;

then the Company shall cause to be filed at each office or agency maintained for
the purpose of exercise of this Warrant, and shall cause to be mailed to the
holder of this Warrant at its address as it shall appear below, at least thirty
(30) calendar days prior to the applicable record or effective date hereinafter
specified, a notice (provided such notice shall not include any material
non-public information) stating (x) the date on which a record is to be taken
for the purpose of such dividend, distribution, redemption, rights or warrants,
or if a record is not to betaken, the date as of which the holders of Common
Stock of record to be entitled to such dividend, distributions, redemption,
rights or warrants are to be determined or (y) the date on which such
reclassification, consolidation, merger, sale, transfer or share exchange is
expected to become effective or close, and the date as of which it is expected
that holders of Common Stock of record shall be entitled to exchange their
shares of Common Stock for securities, cash or other property deliverable upon
such reclassification, consolidation, merger, sale, transfer or share exchange;
provided, however, that the failure to mail such notice or any defect therein or
in the mailing thereof shall not affect the validity of the corporate action
required to be specified in such notice.

                  (h) Adjustment to Exercise Price. If the Company, during the
period commencing on the Closing Date (as defined in the Purchase Agreement)
through and including the date which is 12 months from the Issue Date, takes any
of the actions described in this Section 6(h), then, in order to prevent
dilution of the rights granted under this Warrant, the Exercise Price will be
subject to adjustment from time to time as provided in this Section 6(h);
provided, however, that if (X) (1) the Registration Statement (as


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defined in the Registration Rights Agreement) is then in effect and has been in
effect and sales of all of the Registrable Securities (as defined in the
Registration Rights Agreement) can be made thereunder for at least twenty (20)
Trading Days prior to a Trigger Date; (2) the Company has, at all times prior to
the Trigger Date, a sufficient number of authorized shares of Common Stock
reserved for issuance upon full conversion of all of the Securities (as defined
in the Purchase Agreement) issued pursuant to the Purchase Agreement; and (3) no
Event of Default shall have occurred and be continuing on the Trigger Date or at
any time during the twenty (20) Trading Days prior to a Trigger Date; and (Y)
the Per Share Market Value is greater than 150% of the Conversion Price (as
defined in the Debentures) in effect on the Closing Date (as defined in the
Purchase Agreement) for any five (5) consecutive Trading Days prior to the 180th
day following the Issue Date, then this provision shall expire automatically on
the 180th day following the Issue Date:

                  (i) Adjustment of Exercise Price upon Issuance of Common
         Stock. If, during the period commencing on the Closing Date (as defined
         in the Purchase Agreement) through and including the date which is 12
         months from the Issue Date, the Company issues or sells, or is deemed
         to have issued or sold, any shares of Common Stock (other than the
         Debenture Shares or Warrant Shares (each as defined in the Purchase
         Agreement) or shares of Common Stock deemed to have been issued by the
         Company in connection with a Stock Plan (as defined below), shares of
         Common Stock issuable upon the exercise of any options or warrants
         outstanding on the date hereof or upon conversion of convertible
         securities outstanding on the date hereof, in each case as listed in
         Schedule 2.1(c) of the Purchase Agreement (as defined below), shares of
         Common Stock issued or deemed to have been issued in a Strategic
         Venture (as defined below), or shares of common Stock issued or deemed
         to have been issued as consideration for an acquisition by the Company
         of a division, assets or business (or stock constituting any portion
         thereof) from another person) for a consideration per share (the "New
         Issuance Price") less than $26.95, then immediately after such issue or
         sale, the Exercise Price then in effect shall be reduced to an amount
         equal to 120% of the New Issuance Price. A "Strategic Venture" shall
         mean a venture between the Company and a pharmaceutical or
         biotechnology company or an Affiliate thereof, the primary purpose of
         which is not to raise capital in the form of equity (including without
         limitation through the issuance of warrants, convertible securities,
         phantom stock rights, stock appreciation rights or other rights with
         equity features) and pursuant to which the Company contributes or
         issues securities of the Company valued at less than 50% of the entire
         contribution of the Company. If the Registered Holder and the Company
         cannot agree on the value of the components of such contribution, the
         last two sentences of subsection (F)(I) entitled "Calculation of
         Consideration" shall apply.

                  If, during the period commencing on the Closing Date (as
defined in the Purchase Agreement) through and including the date which is 12
months from the Issue Date, the Company issues or sells, or is deemed to have
issued or sold, any shares of Common Stock (other than Debenture Shares or
Warrant Shares, shares of Common Stock deemed to have been issued by the Company
in connection with a Stock Plan or shares of Common Stock issuable upon the
exercise of any options or warrants outstanding on the date hereof and listed in
Schedule 2.1(c) of the Purchase Agreement) then, for purposes of determining the
adjusted Exercise Price under this Section 6(h)(i), the following shall be
applicable:

                  A. Issuance of Options. If, during the period commencing on
         the Closing Date (as defined in the Purchase Agreement) through and
         including the date which is 12 months from the Issue Date, the Company
         in any manner grants any rights or options to subscribe for or to
         purchase Common Stock or any stock or other securities convertible into


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         or exchangeable for Common Stock (other than the Debenture Shares or
         Warrant Shares or shares of Common Stock deemed to have been issued by
         the Company in connection with a Stock Plan, shares of Common Stock
         issuable upon the exercise of any options or warrants outstanding on
         the date hereof or upon conversion of convertible securities
         outstanding on the date hereof, in each case as listed in Schedule
         2.1(c) of the Purchase Agreement, shares of Common Stock issued or
         deemed to have been issued as consideration for an acquisition by the
         Company of a division, assets or business (or stock constituting any
         portion thereof) from another person or shares of Common Stock issued
         or deemed to have been issued in a Strategic Venture) (such rights or
         options being herein called "Options" and such convertible or
         exchangeable stock or securities being herein called "Convertible
         Securities") and the price per share (the "New Option Price") for which
         Common Stock is issuable upon the exercise of such Options or upon
         conversion or exchange of such Convertible Securities is less than
         $26.95, then the Exercise Price shall be reduced to an amount to equal
         120% of the New Option Price. No adjustment of the Exercise Price shall
         be made upon the actual issuance of such Common Stock or of such
         Convertible Securities upon the exercise of such Options or upon the
         actual issuance of such Common Stock upon conversion or exchange of
         such Convertible Securities.

                  B. Issuance of Convertible Securities. If, during the period
         commencing on the Closing Date (as defined in the Purchase Agreement)
         through and including the date which is 12 months from the Issue Date,
         the Company in any manner issues or sells any Convertible Securities
         and the price per share (the "New Convertible Price") for which Common
         Stock is issuable upon such conversion or exchange (other than the
         Debenture Shares or Warrant Shares or shares of Common Stock deemed to
         have been issued by the Company in connection with a Stock Plan, shares
         of Common Stock issuable upon the exercise of any options or warrants
         outstanding on the date hereof or upon conversion of convertible
         securities outstanding on the date hereof, in each case as listed in
         Schedule 2.1(c) of the Purchase Agreement, shares of Common Stock
         issued or deemed to have been issued as consideration for an
         acquisition by the Company of a division, assets or business (or stock
         constituting any portion thereof) from another person or shares of
         Common Stock issued or deemed to have been issued in a Strategic
         Venture) is less than $26.95, then the Exercise Price shall be reduced
         to equal 120% of the New Convertible Price.

                  C. Change in Option Price or Rate of Conversion. If there is a
         change during the period commencing on the Closing Date (as defined in
         the Purchase Agreement) through and including the date which is 12
         months from the Issue Date in (i) the purchase price provided for in
         any Options, (ii) the additional consideration, if any, payable upon
         the issue, conversion or exchange of any Convertible Securities or
         (iii) the rate at which any Convertible Securities are convertible into
         or exchangeable for Common Stock, then the Exercise Price in effect at
         the time of such change shall be readjusted to the Exercise Price which
         would have been in effect at such time had such Options or Convertible
         Securities still outstanding provided for such changed purchase price,
         additional consideration or changed conversion rate, as the case may
         be, at the time initially granted, issued or sold; provided that no
         adjustment shall be made if such adjustment would result in an increase
         of the Exercise Price then in effect.


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                  D. Certain Definitions. For purposes of determining the
         adjusted Exercise Price under this Section 6(h)(i), the following terms
         have meanings set forth below:

                           (I) "Stock Plan" means any stock or compensation plan
pursuant to which Common Stock may be issued to any employee, officer, director
or consultant of the Company which is either (a) approved by the stockholders of
the Company or (b) approved by the compensation committee of the Company's Board
of Directors for legitimate compensation purposes which provides for the
purchase of the Common Stock at a purchase price of no less than 85% of the
market price of the Common Stock on the date of issuance of such option, warrant
or security.

                           (II) "Common Stock Deemed Outstanding" means, at any
given time, the number of shares of Common Stock issued and outstanding at such
time, plus the number of shares of Common Stock deemed to be outstanding
pursuant to Sections 6(h)(i)(A) and 6(h)(i)(B) hereof regardless of whether the
Options or Convertible Securities are actually exercisable at such time, but
excluding any shares of Common Stock issuable upon exercise of the Warrants.

                  E. Effect on Exercise Price of Certain Events. For purposes of
         determining the adjusted Exercise Price under this Section 6(h)(i), the
         following shall be applicable:

                           (I) Calculation of Consideration Received. If any
Common Stock, Options or Convertible Securities are issued or sold or deemed to
have been issued or sold for cash, the consideration received therefor will be
deemed to be the net amount received by the Company therefor. In case any Common
Stock, Options or Convertible Securities are issued or sold for a consideration
other than cash, the amount of the consideration other than cash received by the
Company will be the fair value of such consideration, except where such
consideration consists of securities, in which case the amount of consideration
received by the Company will be the arithmetic average of the Per Share Market
Values of such security for the five (5) consecutive Trading Days immediately
preceding the date of receipt. In case any Common Stock, Options or Convertible
Securities are issued to the owners of the non-surviving entity in connection
with any merger in which the Company is the surviving entity the amount of
consideration therefor will be deemed to be the fair value of such portion of
the net assets and business of the non-surviving entity as is attributable to
such Common Stock, Options or Convertible Securities, as the case may be. The
fair value of any consideration other than cash or securities will be determined
jointly by the Company and the Registered Owners of a majority of the Warrant
Shares then outstanding. If such parties are unable to reach agreement within
ten (10) days after the occurrence of an event requiring valuation (the
"Valuation Event"), the fair value of such consideration will be determined
within forty-eight (48) hours of the tenth (10th) day following the Valuation
Event by an Appraiser selected by the Company. The determination of such
Appraiser shall be binding upon all parties absent manifest error.

                           (II) Integrated Transactions. In case any Option is
issued in connection with the issue or sale of other securities of the Company,
together comprising one integrated transaction in which no specific
consideration is allocated to such Options by the parties thereto, the Options
will be deemed to have been issued for an aggregate consideration of $.001.


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<PAGE>   10

                           (III) Treasury Shares. The number of shares of Common
stock outstanding at any given time does not include shares owned or held by or
for the account of the Company, and the disposition of any shares so owned or
held will be considered an issue or sale of Common Stock.

                           (IV) Record Date. If the Company takes a record of
the holders of Common Stock for the purpose of entitling them (1) to receive a
dividend or other distribution payable in Common Stock, Options or in
Convertible Securities or (2) to subscribe for or purchase Common stock, Options
or Convertible Securities, then such record date will be deemed to be the date
of the issue or sale of the shares of Common Stock deemed to have been issued or
sold upon the declaration of such dividend or the making of such other
distribution or the date of the granting of such right of subscription or
purchase, as the case may be.

                           (V) Certain Events. If any event occurs of the type
contemplated by the provisions of Section 6(h)(i)(subject to the exceptions
stated therein) but not expressly provided for by such provisions (including,
without limitation, the granting of stock appreciation rights, phantom stock
rights or other rights with equity features), then the Company's Board of
Directors will make an appropriate adjustment in the Exercise Price so as to
protect the rights of the Registered Owner, or assigns, of this Warrant;
provided, however, that no such adjustment will increase the Exercise Price as
otherwise determined pursuant to this Section 6(h).

         In no event shall any provision in this Section 6 cause the Exercise
Price to be greater than the Exercise Price on the date of issuance of this
Warrant.

         7. RESTRICTION ON EXERCISE BY THE REGISTERED OWNER. Notwithstanding
anything in this Warrant to the contrary, in no event shall the Holder of this
Warrant be entitled to exercise a number of Warrants (or portions thereof) in
excess of the number of Warrants (or portions thereof) upon exercise of which
the sum of (i) the number of shares of Common Stock beneficially owned by the
Holder and its affiliates (other than shares of Common Stock which may be deemed
beneficially owned through the ownership of the unexercised Warrants and the
unexercised or unconverted portion of any other securities of the Company
(including the Debentures) subject to a limitation on conversion or exercise
analogous to the limitation contained herein) and (ii) the number of shares of
Common Stock issuable upon exercise of the Warrants (or portions thereof) with
respect to which the determination described herein is being made, would result
in beneficial ownership by the Holder and its affiliates of more than 9.9% of
the outstanding shares of Common Stock. For purposes of the immediately
preceding sentence, beneficial ownership shall be determined in accordance with
Section 13(d) of the Securities Exchange Act of 1934, as amended, and Regulation
13D-G thereunder, except as otherwise provided in clause (i) hereof.
Notwithstanding anything in this Warrant to the contrary, the restriction on
Holder set forth in this paragraph shall not be amended without (i) the written
consent of the Holder and the Company and (ii) the approval of the holders of a
majority of the Company's Common Stock present, or represented by proxy, and
voting at any meeting called to vote on the amendment of such restriction.


                                       10
<PAGE>   11

         8. DEFINITIONS. Capitalized terms used herein and not otherwise defined
herein shall have the meanings given to such terms in the Purchase Agreement. As
used in this Warrant, the following terms have the following meanings:

         "Affiliate" means, with respect to any Person, any other Person that
directly or indirectly controls or is controlled by or under common control with
such Person. For the purposes of this definition, "control," when used with
respect to any Person, means the possession, direct or indirect, of the power to
direct or cause the direction of the management and policies of such Person,
whether through the ownership of voting securities, by contract or otherwise;
and the terms "affiliated," controlling" and "controlled" have meanings
correlative to the foregoing.

         "Appraiser" has the meaning assigned to it in Section 6(c)hereof.

         "Business Day" means any day except Saturday, Sunday and any day which
shall be a legal holiday or a day on which banking institutions in the state of
New York generally are authorized or required by law or other government actions
to close.

         "Common Stock" means the shares of the Company's common stock, par
value $.001 per share.

         "Company" means Geron Corporation, a Delaware corporation.

         "Convertible Securities" has the meaning assigned to it in Section
6(h)(i)(A) hereof.

         "Exercise Period" has the meaning assigned to it the Section 4 hereof.

         "Exercise Price" has the meaning assigned to it in Section 3 hereof.

         "Market Price" has the meaning assigned to it in Section 6(h)(i)
hereof.

         "Options" has the meaning assigned to it in Section 6(h)(i)(A) hereof.

         "Per Share Market Value" means on any particular date (i) the closing
bid price per share of the Common Stock on such date on Nasdaq or another
registered national stock exchange on which the Common Stock is then listed or
if there is no such price on such date, then the closing bid price on such
exchange or quotation system on the date nearest preceding such date, or (ii) if
the Common Stock is not listed then on the National Market System of the Nasdaq
Stock Market or any registered national stock exchange, the closing bid price
for a share of Common Stock in the over-the-counter market, as reported by the
National Quotation Bureau Incorporated (or similar organization or agency
succeeding to its functions of reporting prices) at the close of business on
such date, or (iii) if the Common Stock is not then publicly traded the fair
market value of a share of Common Stock as determined by an Appraiser selected
in good faith by the holder of this Warrant; provided, however, that the
Company, after receipt of the determination by such Appraiser, shall have the
right to select an additional Appraiser, in which case, the fair market value
shall be equal to the average of the determinations by each such Appraiser; and
provided, further that all determinations of the Per Share Market Value shall be
appropriately adjusted for any stock dividends, stock splits or other similar
transactions during such period.


                                       11
<PAGE>   12

         "Purchase Agreement" means that certain Securities Purchase Agreement,
dated June 29, 2000, by and between the Company and the Purchaser (as defined in
the Purchase Agreement).

         "Redemption Event" has the meaning assigned to it in Section 6(f)
hereof.

         "Registered Owner" means RGC International Investors, LDC, or such
other Person as shown on the records of the Company as being the registered
owner of this Warrant.

         "Registration Rights Agreement" means that certain Registration Rights
Agreement, dated as of June 29, 2000, by and between the Company and the Initial
Investor (as defined in the Registration Rights Agreement).

         "Trading Day(s)" means any day on which the primary market on which
shares of Common Stock are listed is open for trading.

         9. REGISTRATION RIGHTS. The Company will undertake the registration of
the Common Stock into which this Warrant is exercisable at such times and upon
such terms pursuant to the provisions of the Registration Rights Agreement.

         10. [INTENTIONALLY OMITTED].

         11. NOTICES. Any notice or other communication required or permitted to
be given hereunder shall be in writing and shall be deemed to have been received
(a) upon hand delivery (receipt acknowledged) or delivery by telex (with correct
answer back received), telecopy or facsimile (with transmission confirmation
report) at the address or number designated below (if received by 8:00 p.m. EST
where such notice is to be received), or the first business day following such
delivery (if delivered on a business day after during normal business hours
where such notice is to be received) or (b) on the second business day following
the date of mailing by express courier service, fully prepaid, addressed to such
address, or upon actual receipt of such mailing, whichever shall first occur.
The addresses for such communications are (i) if to the Company to Geron
Corporation, 230 Constitution Drive, Menlo Park, California 94025 attn: David
Greenwood, fax no. (650) 473-7701 with copies to Latham & Watkins, 135
Commonwealth Drive, Menlo Park, California 94025, Attn: Alan C. Mendelson, Esq.,
fax no. (650) 463-2600 and (ii) if to any Registered Owner to the address set
forth immediately below such Registered Owner's name on the signature pages to
the Purchase Agreement or such other address as may be designated in writing
hereafter, in the same manner, by such Person.

         12. REMEDIES. The Company acknowledges that a breach by it of its
obligations hereunder will cause irreparable harm to the Registered Owner, or
assigns, by vitiating the intent and purpose of the transactions contemplated
hereby. Accordingly, the Company acknowledges that the remedy at law for breach
of its obligations hereunder will be inadequate and agrees, in the event of a
breach or threatened breach by the Company of any of the provisions hereunder,
that the Registered Owner, or assigns, shall be entitled, in addition to all
other available remedies in law or in equity, to an injunction or injunctions to
prevent or cure breaches of the provisions of this Security and to enforce
specifically the terms and provisions hereof, without the necessity of showing
economic loss and without any bond or other security being required.

                            [signature page follows]


                                       12
<PAGE>   13

         IN WITNESS WHEREOF, the Company has caused this Warrant to be executed
by its duly authorized officer as of the date first set forth above.


                                     GERON CORPORATION


                                     By: /s/ DAVID L. GREENWOOD
                                         ---------------------------------------
                                         David L. Greenwood
                                         Senior Vice President, Corporate
                                         Development and Chief Financial Officer


                                       13
<PAGE>   14

                                    EXHIBIT A

                              Warrant Exercise Form

TO:      GERON CORPORATION

         The undersigned hereby: (1) irrevocably subscribes for and offers to
purchase _______ shares of Common Stock of Geron Corporation, pursuant to
Warrant No. ___ heretofore issued to ___________________ on June 29, 2000; (2)
encloses a payment of $__________ for these shares at a price of $________ per
share (as adjusted pursuant to the provisions of the Warrant); and (3) requests
that a certificate for the shares be issued in the name of the undersigned and
delivered to the undersigned at the address specified below. The undersigned
represents that it is an accredited investor within the meaning of Regulation D
under the Securities Act.


                           Date:

                           Investor Name:

                           Taxpayer Identification
                           Number:

                           By:

                           Printed Name:

                           Title:

                           Address:


                           Note:    The above signature should correspond
                                    exactly with the name on the face of this
                                    Warrant Certificate or with the name of
                                    assignee appearing in assignment form below.

AND, if said number of shares shall not be all the shares purchasable under the
within Warrant, a new Warrant Certificate is to be issued in the name of said
undersigned for the balance remaining of the shares purchasable thereunder less
any fraction of a share paid in cash and delivered to the address stated above.