Yes, bobcats range all over South Carolina.
The bobcat (Lynx rufus), also known as the red lynx, is a medium-sized cat native to North America. It ranges from southern Canada through most of the contiguous United States to Oaxaca in Mexico. It is listed as Least Concern on the IUCN Red List since 2002, due to its wide distribution and large population. Although it has been hunted extensively both for sport and fur, populations have proven stable, though declining, in some areas.
It has distinctive black bars on its forelegs and a black-tipped, stubby (or "bobbed") tail, from which it derives its name.