) Eastern ( UTC-4 ) ZIP code 02653 Area code(s) 508 / 774 FIPS code 25-51440 GNIS feature ID 0618257 Website: http://www.town.orleans.ma.us/ Orleans is a town in Barnstable County , Massachusetts , United States . Barnstable County is coextensive with Cape Cod . The population was 6,341 at the 2000 census.