Federal law prohibits hand gun ownership by anyone under the age of 18.
The issue for long guns (rifle's and shot guns typically used for hunting) is cloudier, and varies from state to state.
https://www.washingtonpost.com/news...own-a-rife-or-shotgun/?utm_term=.365b377b6a4e
The ones with no minimum make my state (NY look almost sane with having it at 16). Illinois is the only one that has it at 21. You see mostly the usual suspects with non minimum age, but then you notice California, Massachusetts, Connecticut on the list. Maine, Vermont and New Hampshire are a little surprising except for the hunting aspect. Idaho is surprise the other way, as is Florida and Oklahoma, they have gone with 18.
So yes in most states a 13 year old could own a rifle. But there are also federal and state laws limiting who can buy a long gun. So a 13 year might be able to own one, but not buy one themselves (they would have to say have it given to them by a relative). yes it is crazy.