[jMyles]

People in the United States on tourist visas are not prohibited from bearing arms (in fact gun ranges are major tourist destinations in some parts of the country). Purchasing arms is subject to a higher legal standard, but is also not wholesale prohibited, just subject to a few extra rules. For example, a tourist who acquires a hunting license in any state can purchase a firearm.

...and in any case, this is not a citizen/non-citizen issue, as GP claims - lawful permanent residents have the same 2nd amendment rights as citizens.