Sen. John Thune (R-S.D.) is a co-sponsor.
Tester's bill also allows the transportation of bows on national parks.
In April, the House introduced legislation that also legalized importation of polar bear trophies. That bill, the Sportsman's Heritage act, H.R. 4089, also eases a number of laws related to using firearms on federal lands.
Senators have been quick to offer amendments to the farm bill since the chamber began consideration of it on Tuesday. Many of those amendments were not directly related to the farm bill and could pose a problem to passing the legislation. The chamber has only been able to pass recent legislation after reaching an agreement over which amendments and how many to consider.
If the Senate does not agree to which amendments to consider on the farm bill, it could stall in the chamber despite having bipartisan support.