Escobedo was founded in 1964. The team played in the regional leagues for the vast majority of its first 26 years, with the one exception being a season-long stay in Tercera División in 1967–68.
The team returned to the category, now the national fourth division, twenty-one years later, remaining there for the subsequent decades. In 1991–92 and the following campaigns it was crowned division champions, adding four runner-up places; however, none of the ten promotion playoff visits to Segunda División B was successful.
Escobedo’s home ground is the Estadio Eusebio Arce, around a mile west of Muriedas, the capital of Camargo. It has a capacity of 2,000 seats with a low, cantilevered stand that runs the length of the pitch on the north side of the enclosure. The stand also houses the players changing facilities, club offices and a social club.