Rhine is a town in Dodge County, Georgia, United States. The population was 295 in 2020. A post office called Rhine was established in 1890. …Rhine is a town in Dodge County, Georgia, United States. The population was 295 in 2020. A post office called Rhine was established in 1890. The community was named after the Rhine river, in Germany, the native land of a large share of the first settlers. The Georgia General Assembly incorporated Rhine as a town in 1891.