Did a quick search before posting. Nowhere, did I see in the regulations or permitting/licensing any mention of releasing gamebirds on private property or otherwise public land.
You will most likely have to contact you're local game warden to find out what permits, licenses or other paperwork that would be required to release gamebirds in your state.
The only thing I could find is the requirements to operate a hunting preserve. https://www.clemson.edu/public/lph/ahp/poultry-npip/game-bird-farm.html
Most likely they, the SCDNR doesn't allow for private citizens to release gamebirds within the state.
Good luck in you're endeavors.