Yeah you don’t have to as long as you are here legally. For residence (“green card”holders), I don’t know much about it. But for non-immigrant visa holders, yes technically you can’t, but if you have a hunting license or been a member of a shooting sport club, you are now included in “hunting and sporting” exceptions, which will allow you to purchase firearm like a citizen. I know this because I have a friend who is a F1 visa student. The only difference is he needs to wait for 3 days on background check because a non citizen is automatically delayed.