The leaves don't really look like Clematis terniflora (sweet autumn clematis, the invasive one), but I'm no expert. There are a number of native clematis species.
You might try asking on the Name That Plant! forum. Also there's a Georgia Native Plant Society group on FB that might be able to help as well. We have a similar one for Missouri and it seems like the members of our group can identify just about anything that occurs in Missouri.