Elgin is a city mostly in Bastrop County and partly in Travis County, Texas, United States. The population was 5,700 at the 2000 census. By 2005, the population grew to an estimated 8,689. Also known as The Sausage Capital of Texas. Elgin apartments for rent comparison page shows most up to date rent information on Elgin apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.