The answer is yes, with some restrictions. To understand Indiana's "Taser" law (IC 35-47-8) let's review the terminology used by the state legislature that defines what an energy weapon is.
Indiana recognizes three types of energy weapons:
Stun Gun: Mechanism that delivers a shock equal to but not in excess of (5) milliamps at sixty (60) hertz.Electronic Stun Weapon: Mechanism that delivers a shock in excess of five (5) milliamps at sixty (60) hertz.Taser: Mechanism that delivers a shock by means of a projectile.
Indiana’s Handgun Law (IC 35-47-2) applies to Electronic Stun Weapons and Tasers, but not to Stun Guns.
If you want to carry a Taser or Electronic Stun Weapon in public, you must have a handgun permit.  If you are a convicted felon, you cannot possess a Taser or Electronic Stun Weapon.  No one under 18 year of age may possess any type of energy weapon.