Rockport is a city in Hot Spring County in the U.S. state of Arkansas. As of the 2010 census, the population of Rockport was 755, down from 79…Rockport is a city in Hot Spring County in the U.S. state of Arkansas. As of the 2010 census, the population of Rockport was 755, down from 792 in 2000. Rockport is one of the oldest named places in Arkansas. Although the present city is overshadowed by Malvern, Rockport served as the county seat of Hot Spring County from 1846 to 1879 and was a landmark community of Arkansas for many years both before and after that time.