Generally, Indiana allows anyone to buy a car if they have the financial mean. If you are currently living in Indiana you will need to register the vehicle there as well. When you go to register the car in Indiana you will need a certificate of Origin, Odometer Statement, Proof of Insurance and Verification of Social Security Number.
If you do not have a social security number you will not be able to register the vehicle in Indiana. Without the car being registered it would not be allowed to be driven on the IN roadways.
For more information regarding how to register and title a vehicle in Indiana contact the IN Bureau of Motor Vehicles.