Sponsored Topics. Asheboro is a city in Randolph County, North Carolina, United States. The population was 21,672 at the 2000 census. It is the county seat of Randolph County, and is the home of the state-owned North Carolina Zoo. Asheboro is located at 35°42′55″N 79°48′47″W / 35.71528°N 79.81306°W / 35.71528; -79.81306 (35.715211, -79.813001).