There are 12 US Post Offices in Spencer County serving a total of 20,020 residents equating to 1,668 residents per post office. It's estimated that approximately 31,954 packages are handled across the 12 county post offices annually. Spencer County is a county located in the U.S. state of Indiana. As of the 2010 census, the population was 20,952. The county seat is Rockport."