Randolph Township is one of four townships in Ohio County, Indiana, United States. As of the 2020 census, its population was 4,307 and it contained 2,008 housing units. According to the 2010 census, the township has a total area of 38.54 square miles, of which 37.34 square miles is land and 1.21 square miles is water. The Ohio River defines t…Randolph Township is one of four townships in Ohio County, Indiana, United States. As of the 2020 census, its population was 4,307 and it contained 2,008 housing units. According to the 2010 census, the township has a total area of 38.54 square miles, of which 37.34 square miles is land and 1.21 square miles is water. The Ohio River defines the township's eastern border.