Delmita is a census-designated place in Starr County, Texas, United States. Its elevation is 272 feet. Although Delmita is unincorporated, it has a post office, with the ZIP code of 78536. This CDP was new for the 2010 census, with a population of 216. The community was founded as Zaragosa in 1919, then was changed to Delmita on April 1, 1931 because of confusion with the Reeves County community of Saragosa.