This code stands for 'U S Army' and the 'F' is a procurement instrument identifier code.

Google ...'ACQUISITION.GOV' Subpart 4.1603 Procedures (a)(3)(vi) and you will see The Instrument and the Letter Designation F. The description is - task orders, delivery orders or calls under indefinite-delivery including blanket purchase agreements; or basic ordering agreements.

I own a Rochester Ordinance Depot shotgun marked with USA-F too. It was shipped to the Ordinance Depot on Order No. 52308.