As for the one that said you cannot own an rpg, that is false. In fact, any U.S. citizen can obtain even tanks if they file the proper paperwork. Although, your state has separate regulations (California is pretty strict).
Depends on State laws. Federally, machine guns are registered under the National Firearms Act of '34, and to be legally transferable for civilian ownership it needs to have been registered before the registry closed in 1986. $200 tax and a Form 4 to register.
For an RPG, it'd be an Explosive Destructive Device... assuming it was legally imported, again, $200 and a Form 4.
Let's say you could get somebody to sell you an Abrams, roll-away, just as a thought experiment. The coaxial 7.62 and the commander's hatch gun would be illegal MG's and have to be scrapped, the main gun at greater than 1/2" bore and no sporting purpose is a Large Bore Destructive Device ($200 and a Form 4), and each shell is an Explosive DD (which means $200 and a Form 4 EACH). And, oh by the way, you ALSO have to make sure it's kosher under all State and Local laws too...
EDIT: You can buy an RPG under the National Firearms Act as a "Destructive Device", following an FBI/BATF background check and the receipt of a 200.00 tax.