Yes. All nonimmigrant aliens (with a few exceptions ) must obtain an import permit from ATF to temporarily import firearms and ammunition for hunting or other lawful sporting purposes. Please note this requirement applies to all nonimmigrant aliens, not all nonresidents (e.g., it does not apply to U.S. citizens residing abroad).
The form to be filed with ATF is an ATF Form 6 NIA (5330.3D) (Application/Permit for Temporary Importation of Firearms and Ammunition by Nonimmigrant Aliens) with documentation demonstrating that you fall within an exception to the nonimmigrant alien prohibition. The form is both the application and, once approved, the permit you present to the U.S. Customs and Border Protection when you enter the United States. The Form 6 NIA can be downloaded at www.atf.gov.
[27 CFR 478.115(d) and (e) and 478.120]