There also is no ruling that you CAN!
The Heller decision
http://en.m.wikipedia.org/wiki/District_of_Columbia_v._Heller
Held that owning a gun or long rifle, outside of militia, per the 2nd Amendment, is only allowed for self protection at home, and must be kept unloaded, and that the right s not absolute, and there is no mentioning of shit like the type of weapon the AR 15 and similar are.
Furthermore, any attempts since then to include them, too, HAVE FAILED!!!!!!
And there have been many.