I thought there was a way to do that, but my info was old and I may have been mistaken (thus this edit).
The following is the only info I can find on this subject from an official source:
R. NONIMMIGRANT ALIENS
(R1) May nonimmigrant aliens legally in the United States purchase or possess firearms and ammunition while in the United States?
Nonimmigrant aliens generally are prohibited from possessing or receiving (purchasing) firearms and ammunition in the United States.
There are exceptions to this general prohibition. The exceptions are as follows:
1. nonimmigrant aliens who possess a valid (unexpired) hunting license or permit lawfully issued by a State in the United States;
2. nonimmigrant aliens entering the United States to participate in a competitive target shooting event or to display firearms at a sports or hunting trade show sponsored by a national, State, or local firearms trade organization devoted to the collection, competitive use or other sporting use of firearms;
3. certain diplomats, if the firearms are for official duties;
4. officials of foreign governments, if the firearms are for official duties, or distinguished foreign visitors so designated by the U.S. State Department;
5. foreign law enforcement officers of friendly foreign governments entering the United States on official law enforcement business; and
6. persons who have received a waiver from the prohibition from the U.S. Attorney General.
Significantly, even if a nonimmigrant alien falls within one of these exceptions, the nonimmigrant alien CANNOT purchase a firearm from a Federal firearms licensee (FFL) unless he or she (1) has an alien number or admission number from the Department of Homeland Security (formerly the Immigration and Naturalization Service) AND (2) can provide the FFL with documentation showing that he or she has resided in a State within the United States for 90 consecutive days immediately prior to the firearms transaction.
[18 U.S.C. 922(g)(5)(b) and 922(y), 27 CFR 478.124, ATF Rul. 2004-1]