Kerry's signature made the United States the 89th country to sign the Arms Trade Treaty, which aims to regulate international trade in conventional weapons, The Hill rep roted.
"Any act to implement this treaty, provisionally or otherwise, before the Congress provides its advice and consent would be inconsistent with the United States Constitution, law, and practice," Corker added.
In March, an amendment filed by Sen. James Inhofe, R-Okla., to the Senate budget received 53 "yes" votes.
Kerry announced in June the administration would sign the treaty.
The National Rifle Association has termed the ATT a plan by the United Nations to seize Americans' weapons.
Advocates of the treaty say the treaty is intended to regulate cross-border gun sales to keep weapons out of the hands of terrorists.
Oxfam America president Raymond Offenheiser called the U.S. action "a powerful step demonstrating the United States' commitment to preventing mass atrocities and protecting civilians from armed conflict. We hope that the U.S. signing will lead other major exporters to get off the fence and sign the ATT as soon as possible."