The regulations on armor piercing ammo are among the strangest of the federal firearms regulations. The first is that AP ammo is rather odd in its definition. The ATF defines it as handgun ammunition, but there’s a catch. If any handgun has ever been made in a specific caliber, then ATF considers that the AP ammo regulations then apply to that caliber. That’s why you can’t buy AP ammo for cartridges like 7.62×39 and several others. The 5.56x45NATO is specifically exempted from this, even though there are pistols made for it.
It’s perfectly legal to possess, purchase, sell or shoot armor piercing ammunition. It’s not legal to manufacture or import armor piercing ammunition.
In order to manufacture AP rounds, you have to hold a type 10 FFL (18 USC sec. 922(a)(7)). In order to import AP rounds, you have to hold a type 11 FFL (18 USC sec. 922(a)(7)). If you hold either one of these FFLs, it’s not legal to sell or export AP rounds, except to military, law enforcement (18 USC sec. 922(a)(8)). In addition, if you hold a type 06-08 FFL (manufactures of firearms, importers of firearms, manufactures of ammunition), then you also my not sell AP rounds to the general public.
For regular type 01-03 FFL holders, you may sell or deliver AP ammunition, but it must be entered into the Acquisition and Disposition Record (bound book). So if you have any AP rounds in your possession, that’s ok. But it’s been illegal to manufacture or import new ammunition that’s transferable to ordinary citizens for quite some time, and for the most part, it’s generally unavailable, and certainly not in any significant quantity for most calibers.
Of course, there are also various state restrictions. Pennsylvania prohibits KTW ammunition. NJ and NY have additional restrictions on AP ammo.