Clinch County is a county located in the U.S. state of Georgia. As of the 2010 census, the population was 6,798. The county seat is Homerville. The county was created on February 14, 1850, named in honor of Duncan Lamont Clinch.With just 8.5 people per square mile (land), Clinch has one of the lowest population densities of any county in Georgia.