Founded in 1971 by Dionisio Muñoz Jerez. The founding act of the club was signed on 20 July that year. Alcorcón spent roughly its first 30 years of existence in between the fourth division and the regional leagues. Alcorcón played its first match on 8 September 1971 against Atlético Madrid (youth team) and lost it 0:2. In 2000–01, it made its Segunda División B debut, finishing in 12th place, and spending the following seasons immersed in mid-table positions. The 2003–04 season Alcolcórn led by coach Raúl González finished in 10th position in Segunda División B.
In 2008–09, a third place in the regular season meant Alcorcón was allowed to appear in the promotion play-offs for the first time in its history. After disposing of Sant Andreu and Alcoyano, the club was ousted by Real Unión of Irun in the final round with a 3–1 aggregate scoreline.
On 10 November, in the second leg at the Santiago Bernabéu, the club lost 1–0, but won 4–1 on aggregate, thereby going through to the next round of 16, where the club was ousted by Racing de Santander, 2–3 on aggregate.
In 2017, Alcorcón qualified to the Copa del Rey quarter-finals for the first time in their history after a penalty shoot-out victory over Espanyol, but were beaten 2–0 on aggregate by Alavés. The club was 13th in the 2017–18 season in the Segunda División, just 4 points away from being relegated, and also struggled in the next campaign, but retained its place in Segunda División after finishing the season in the 14th position.