I am an Indian passport holder about to go on an internship program in Iran. If I get any future opportunities in the US, will I be able to go and study there? Or will I be denied entry into the states?
The formal restriction on visiting the USA after having visited Iran applies only to the Visa Waiver Program. Persons who have traveled to Iran are still able to get a US visa, and in fact are required to if they would otherwise have been eligible for the VWP.
Citizens of India are not eligible for the VWP and require a visa in any case. Therefore, the formal restriction against retaining VWP eligibility after having visited Iran does not apply to you. You can still get a US visa. You may, however, have a difficult time in the visa interview, but the US official will not necessarily deny you a US visa for having visited Iran. The fact of your Iran visit will simply be one piece of data that the official may or may not consider relevant.