You can only open carry a firearm in certain conditions.
That firearm must be able to be used in a currently open hunting season.
The ammo in said firearm must be able to be used in a currently open hunting season.
You must be traveling between your hunting area and your vehicle/home.
As deer season use over, you can't open carry a rifle as it's not deer/squirrel season and rifles aren't permitted for hunting outside of those seasons.
If it's turkey season, you can carry a shotgun but you may Not being possession of any shot larger than shot size number two (IIRC). If you're found with a shotgun and one shell of buckshot, you can get fined and possibly lose your firearm.
You need to consult an SCDNR figurine book. They're free at most places which sell hunting/fishing licenses.
It may or may not be legal but is certainly not a good idea to open carry a rifle walking down the street or into public park, a mall, store, whatever. It is a sure fire way to quickly meet your local SWAT team.