Swifton is a city in Jackson County, Arkansas, United States. The mayor is Craig Crider. The population was 798 at the 2010 census. Swifton wa…Swifton is a city in Jackson County, Arkansas, United States. The mayor is Craig Crider. The population was 798 at the 2010 census. Swifton was the hometown of Baseball Hall of Famer George Kell. According to the United States Census Bureau, the city has a total area of 0.54 square miles, all land.