The statute puts liability on the owner
S.C. Code 47-3-110 provides that if a person is bitten or otherwise attacked by a dog in a public place or lawfully in a private place, including the property of the dog owner or other person having the dog in his care or keeping, the owner or keeper is liable for the damages suffered. Provocation and trespass are the usual defenses.
The statute of limitations is three years under S.C. Code 15-3-530.