Williamstown is a city in Grant county in the U.S. state of Kentucky. The population was 3,227 as of the 2000 census. It is the county seat of Grant County. When Grant County was formed in 1820, William Arnold offered land for the county seat. Arnold was a veteran of the Revolutionary War and settled the area in 1795. The town built there was named after him when it incorporated in 1825. The county grew slowly, reaching a population of just 281 by 1870.