It all depends on what you want to hunt and where.
Each state will have a web page for that state's "Game and Wildlife" laws, seasons and licenses needed.
I just had a fella come over from Germany the first part of February to predator hunt with me. He purchased a no-resident 5 day small game license for $48 and hunted predators for the week. That license also allowed exotic hunting and he went to a game ranch like longspur mentioned and took a nice blackbuck antelope.
It take a bit of planning but it is possible!