<PAGE>

                                  Exhibit 4.4
                                  -----------

THIS WARRANT AND THE SECURITIES ISSUABLE UPON EXERCISE OR CONVERSION HEREOF HAVE
NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY
APPLICABLE STATE LAWS, AND NO INTEREST THEREIN MAY BE SOLD, DISTRIBUTED,
ASSIGNED, OFFERED, PLEDGED OR OTHERWISE TRANSFERRED UNLESS (I) THERE IS AN
EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT AND APPLICABLE STATE SECURITIES
LAWS COVERING ANY SUCH TRANSACTION OR SUCH TRANSACTION IS EXEMPT FROM THE
REGISTRATION REQUIREMENTS OF SUCH ACT AND LAWS AND (II) SUCH TRANSFER IS
EFFECTED IN ACCORDANCE WITH THE TERMS SET FORTH IN THIS WARRANT.


No.  1-REV                        RAMBUS INC.                    January 7, 1997
   ---------                                                     ---------


                         COMMON STOCK PURCHASE WARRANT


     This certifies that, for good and valuable consideration, Intel Corporation
("Intel"), or registered assigns, is entitled, upon the terms and subject to the
conditions hereinafter set forth, to acquire from Rambus Inc., a California
corporation (the "Company"), in whole or from time to time in part, up to one
million (1,000,000) fully paid and nonassessable shares of Common Stock of the
Company ("Warrant Stock") at a purchase price per share of ten dollars ($10.00)
(the "Exercise Price").  Such number of shares, type of security and Exercise
Price are subject to adjustment as provided herein, and all references to
"Warrant Stock" and "Exercise Price" herein shall be deemed to include any such
adjustment or series of adjustments.

     1.   Exercise of Warrant

          (a)  Vesting Time. The term "Vesting Time" means the close of business
               ------------
on the last day of the first two-calendar quarter period in which more than
twenty percent (20%) of the main memory chipsets shipped by Intel in each
calendar quarter in such period implemented the Rambus-1 Interface Specification
or the Rambus-2 Interface Specification.

          (b)  Expiration Time. The term "Expiration Time" means the close of
               ---------------
business on the eighth (8th) anniversary of the date hereof; provided, however,
                                                             -------- --------
that if the Vesting Time shall not have occurred on or prior to twelve (12)
months following the Success Determination Date (as such term is defined in the
Semiconductor Technology License Agreement between Intel and the Company), then
the term "Expiration Time" shall mean the close of business on the date twelve
(12) months following the Success Determination Date.

          (c)  Exercise Procedure.  The purchase rights represented by this
               ------------------
Warrant are exercisable, in whole or in part, at any time and from time to time
at or after the Vesting Time and at or prior to the Expiration Time, by the
surrender of this Warrant and the Notice of Exercise form attached hereto duly
executed to the office of the Company at 2465 Latham Street, Mountain View, CA
94040, Attn: Corporate Secretary (or such other office or agency of the Company
as it may designate by notice in writing to the registered holder hereof at the
address of such holder appearing on the books of the Company), and upon payment
of the Exercise Price for the shares thereby purchased (by wire transfer or by
certified bank check payable to the order of the Company, by cancellation of
indebtedness of the Company to the holder hereof, if any, at the time of
exercise,
<PAGE>

or by any combination thereof, in an amount equal to the purchase price of the
shares thereby purchased); whereupon the holder of this Warrant shall be
entitled to receive from the Company a stock certificate in proper form
representing the number of shares of Warrant Stock so purchased, and a new
Warrant in substantially identical form for the purchase of that number of
shares of Warrant Stock equal to the difference, if any, between the number of
shares of Warrant Stock subject hereto and the number of shares of Warrant Stock
as to which this Warrant is so exercised.

     2.   Conversion of Warrant

     The registered holder hereof shall have the right to convert this Warrant,
in whole or in part, at any time and from time to time at or after the Vesting
Time and at or prior to the Expiration Time, by the surrender of this Warrant
and the Notice of Conversion form attached hereto duly executed to the office of
the Company at the address set forth in Section 1(c) hereof (or such other
office or agency of the Company as it may designate by notice in writing to the
registered holder hereof at the address of such holder appearing on the books of
the Company), into shares of Warrant Stock as provided in this Section 2.  Upon
exercise of this conversion right, the holder hereof shall be entitled to
receive that number of shares of Warrant Stock of the Company equal to the
quotient obtained by dividing [(A - B)(Y)] by (A), where:

     A    =    the Fair Market Value (as defined below) of one share of Warrant
               Stock on the date of conversion of this Warrant;

     B    =    the Exercise Price for one share of Warrant Stock under this
               Warrant; and

     Y    =    the number of shares of Warrant Stock as to which this Warrant is
               being converted.

     If the above calculation results in a negative number, then no shares of
Warrant Stock shall be issued or issuable upon conversion of this Warrant.

     "Fair Market Value" of a share of Warrant Stock shall mean:

     (a)  if the conversion right is being exercised in connection with a
          transaction specified in Section 10(b) hereof, the value of the
          consideration (determined, in the case of noncash consideration, in
          good faith by the Board of Directors of the Company) to be received
          pursuant to such transaction by the holder of one share of Warrant
          Stock;

     (b)  if the conversion right is being exercised in connection with the
          initial public offering of the Company's Common Stock, the initial
          public offering price (before deducting commissions, discounts or
          expenses) at which the Common Stock is sold in such offering;

     (c)  if the conversion right is being exercised more than five (5) business
          days after the occurrence of the initial public offering of the
          Company's Common Stock:

                    (i)  if the Company's Common Stock is traded on an exchange
          or is quoted on the National Association of Securities Dealers, Inc.
          Automated Quotation ("NASDAQ") National Market System, the average of
          the closing or last sale price reported for the five (5) business days
          immediately preceding the date that the Notice of Conversion is
          delivered to the Company;

                                      -2-
<PAGE>

                    (ii)  if the Company's Common Stock is not traded on an
          exchange or on the NASDAQ National Market System, but is traded in the
          over-the-counter market, the mean of the closing bid and asked prices
          reported for the five (5) business days immediately preceding the date
          that the Notice of Conversion is delivered to the Company; and

     (d)  in all other cases, the fair value as determined in good faith by the
          Company's Board of Directors.

     Upon conversion of this Warrant in accordance with this Section 2, the
registered holder hereof shall be entitled to receive a certificate for the
number of shares of Warrant Stock determined in accordance with the foregoing,
and a new Warrant in substantially identical form for the purchase of that
number of shares of Warrant Stock equal to the difference, if any, between the
number of shares of Warrant Stock subject hereto and the number of shares of
Warrant Stock as to which this Warrant is so converted.

     3.   Issuance of Shares; No Fractional Shares or Scrip

     Certificates for shares purchased hereunder or issuable upon conversion
hereof shall be delivered within a reasonable time after the date on which this
Warrant shall have been exercised or converted in accordance with the terms
hereof. The Company hereby represents and warrants that all shares of Warrant
Stock which may be issued upon the exercise or conversion of this Warrant will,
upon such exercise or conversion, be duly and validly authorized and issued,
fully paid and nonassessable and free from all taxes, liens and charges in
respect of the issuance thereof (other than liens or charges created by or
imposed upon the holder of the Warrant Stock). The Company agrees that the
shares so issued shall be and shall for all purposes be deemed to have been
issued as of the close of business on the date on which this Warrant shall have
been exercised or converted in accordance with the terms hereof. No fractional
shares or scrip representing fractional shares shall be issued upon the exercise
or conversion of this Warrant. With respect to any fraction of a share called
for upon the exercise or conversion of this Warrant, an amount equal to such
fraction multiplied by the Fair Market Value of a share of Warrant Stock on the
date of exercise or conversion shall be paid in cash or check to the holder of
this Warrant.

     4.   Charges, Taxes and Expenses

     Issuance of certificates for shares of Warrant Stock upon the exercise or
conversion of this Warrant shall be made without charge to the holder hereof for
any issue or transfer tax or other incidental expense in respect of the issuance
of such certificate, all of which taxes and expenses shall be paid by the
Company, and such certificates shall be issued in the name of the holder of this
Warrant.

     5.   No Rights as a Shareholder

     This Warrant does not entitle the holder hereof to any voting rights or
other rights as a shareholder of the Company prior to the exercise or conversion
hereof.

     6.   Restrictions on Transfer; Lock-Up

          (a)  Transfer of Warrant.  Prior to the Expiration Time and subject to
               -------------------
compliance with applicable laws, this Warrant and all rights hereunder are
transferable by the holder hereof, in whole or in part, at the office or agency
of the Company referred to in Section 1(c) hereof. Any such transfer shall be
made upon surrender of this Warrant together with the Assignment Form attached
hereto properly executed, endorsed and guaranteed. Notwithstanding the
foregoing, the Company may prohibit the transfer of this Warrant and the rights

                                      -3-
<PAGE>

hereunder to more than a single transferee or to a transferee which the Company
reasonably believes to be an actual or potential competitor of the Company.  The
Company shall not be required to effect any transfer of this Warrant or the
rights hereunder unless the transferor and transferee provide the Company with
an opinion of counsel that such transfer is in compliance with applicable
Federal and state securities laws, or provide the Company with information
sufficient for the Company or the Company's counsel to make such determination.
The Company shall not be required to effect any transfer of this Warrant or the
rights hereunder unless the transferee shall have agreed in writing to be bound
by the restrictions set forth in this Warrant.

          (b)  Transfer of Warrant Stock.  Prior to the closing of the initial
               -------------------------
public offering of the Company's Common  Stock pursuant to a registration
statement declared effective under the Securities Act of 1933, as amended (the
"Securities Act"), the Company may prohibit the transfer of the Warrant Stock to
more than a single transferee or to a transferee which the Company reasonably
believes to be an actual or potential competitor of the Company. The Company
shall not be required to effect any transfer of the Warrant Stock unless the
transferor and transferee provide the Company with an opinion of counsel that
such transfer is in compliance with applicable Federal and state securities
laws, or provide the Company with information sufficient for the Company or the
Company's counsel to make such determination.  The Company shall not be required
to effect any transfer of the Warrant Stock unless the transferee shall have
agreed in writing to be bound by the restrictions set forth in this Warrant.

          (c)  Lock-Up.  In connection with any registration of the offering of
               -------
any securities of the Company under the Securities Act, if so requested by the
Company or any representative of the underwriters (the "Managing Underwriter"),
the Warrant, the Warrant Stock and any securities of the Company issued with
respect thereto, and any interest therein, may not be sold, transferred or
otherwise disposed of during the period specified by the Company's Board of
Directors at the request of the Managing Underwriter, with such period not to
exceed 180 days following the effective date of a registration statement of the
Company filed under the Securities Act (the "Market Standoff Period"). The
Company may impose stop-transfer instructions with respect to securities subject
to the foregoing restrictions until the end of such Market Standoff Period. The
restrictions set forth in this Section 6(c) shall be of no further force or
effect following the transfer of the securities subject hereto pursuant to a
registration statement filed under the Securities Act or pursuant to a brokers'
transaction or transaction with a market maker pursuant to Rule 144 promulgated
under the Securities Act.

          (d)  No Public Market.  At the date of issuance of this Warrant, no
               ----------------
public market exists for any of the securities of the Company and the Company
makes no assurances that a public market will ever exist for the Company's
securities.

          (e)  Legends.  The certificates representing the Warrant Stock and any
               -------
securities of the Company issued with respect thereto shall be imprinted with
legends restricting transfer except in compliance with the terms hereof and with
applicable Federal and state securities laws.

     7.   Exchange and Registry of Warrant

     The Company shall maintain at the office or agency referred to in Section
1(c) hereof a registry showing the name and address of the registered holder of
this Warrant.  This Warrant may be surrendered for exchange, transfer, exercise
or conversion, in accordance with its terms, at such office or agency of the
Company, and the Company shall be entitled to rely in all respects upon such
registry.

                                      -4-
<PAGE>

     8.   Loss, Theft, Destruction or Mutilation of Warrant

     On receipt by the Company of evidence reasonably satisfactory to the
Company of the loss, theft, destruction or mutilation of this Warrant, and in
case of any such loss, theft or destruction of this Warrant, on delivery of an
indemnity agreement reasonably satisfactory in form and amount to the Company
or, in the case of any such mutilation, on surrender and cancellation of such
Warrant, the Company will execute and deliver to the holder, in lieu thereof, a
new Warrant in substantially identical form.

     9.   Saturdays, Sundays and Holidays

     If the last or appointed day for the taking of any action or the expiration
of any right required or granted herein shall be a Saturday or a Sunday or shall
be a legal holiday, then such action may be taken or such right may be exercised
on the next succeeding business day.

     10.  Adjustment to Number and Type of Securities and Exercise Price

     The type and number of securities of the Company issuable upon exercise of
this Warrant and the Exercise Price are subject to adjustment as set forth
below:

          (a)  Adjustment for Stock Splits, Stock Dividends, Recapitalizations,
               ----------------------------------------------------------------
Automatic Conversion, etc..  The Exercise Price and the number and type of
--------------------------
securities and/or other property issuable upon exercise of this Warrant shall be
appropriately and proportionately adjusted to reflect any stock dividend, stock
split, combination of shares, reclassification, recapitalization, automatic
conversion, redemption or other similar event affecting the number or character
of outstanding shares of Warrant Stock, so that the number and type of
securities and/or other property issuable upon exercise of this Warrant shall be
equal to that which would have been issuable with respect to the number of
shares of Warrant Stock subject hereto at the time of such event, had such
shares of Warrant Stock then been outstanding.

          (b)  Adjustment for Reorganization, Consolidation, Merger, etc..  In
               ----------------------------------------------------------
case of any consolidation or merger of the Company with or into any other
corporation, entity or person, or any other corporate reorganization, in which
the Company shall not be the continuing or surviving entity of such
consolidation, merger or reorganization (any such transaction being hereinafter
referred to as a "Reorganization"), then, in each case, the holder of this
Warrant, on exercise or conversion hereof at any time after the consummation or
effective date of such Reorganization, shall receive, in lieu of the Warrant
Stock issuable on such exercise prior to the date of such Reorganization, the
stock and other securities and property (including cash) to which such holder
would have been entitled upon the date of such Reorganization if such holder had
exercised this Warrant immediately prior thereto.

          (c)  Adjustment for Right of First Refusal.  In case of any event
               -------------------------------------
which, under the terms of the Rambus Inc. Amended and Restated Information and
Registration Rights Agreement dated of even date herewith, as such may be
amended from time to time (the "Rights Agreement"), would have entitled Intel
Corporation to exercise its Right of First Refusal (as defined in Section 7 of
the Rights Agreement) if the Warrant Stock had been held by Intel Corporation on
the date of such event, then the holder of this Warrant, upon exercise or
conversion hereof at any time after the date of such event, may elect to
purchase (in addition to the Warrant Stock) the type and number of securities
which Intel Corporation would have been so entitled to purchase, and upon such
election shall pay to the Company (in addition to the Exercise Price) the
consideration which Intel Corporation would have been required to pay in
connection with the exercise of such a Right of First Refusal.

                                      -5-
<PAGE>

The provisions of this Section 10(c) shall apply to any partial exercise or
conversion of this Warrant on a pro rata basis.

          (d)  Certificate as to Adjustments.  In case of any adjustment in the
               -----------------------------
Exercise Price or number and type of securities issuable on the exercise of this
Warrant, the Company will promptly give written notice thereof to the holder of
this Warrant in the form of a certificate, certified and confirmed by an officer
of the Company, setting forth such adjustment and showing in reasonable detail
the facts upon which such adjustment is based.

                                      -6-
<PAGE>

     11.  Governing Law

     This Warrant shall be governed by and construed in accordance with the laws
of the State of California.

     IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by
its duly authorized officer.

                                   RAMBUS INC.,
                                   a California corporation


                                   By: /s/ Gary Harmon
                                       ---------------------------------------

                                   Name: Gary Harmon
                                        --------------------------------------

                                   Title:  V. P.
                                         -------------------------------------