If you live in Georgia and buy a used car from a dealer in SC do you have to pay sales tax?

Yes, if you take delivery of an item in another state the merchant there MUST collect sales tax there. If the merchant ships it to you out of state via 'common carrier' the merchant does not have an obligation to collect Georgia sales tax, but YOU have the burden to pay the USE tax and you will pay the use tax when you go to register the car.