Butler is a home rule-class city in Pendleton County, Kentucky, in the United States. The population was 612 at the 2010 census. Accordin…Butler is a home rule-class city in Pendleton County, Kentucky, in the United States. The population was 612 at the 2010 census. According to the United States Census Bureau, Butler has a total area of 0.2 square miles, of which 0.2 square miles is land and 4.17% is water.