Borja also represented Mexico in international competition from 1966 to 1975. He played in 65 games and scored 31 goals making him the 6th all-time leading scorer for Mexico. He played for Mexico in the World Cups in 1966 and 1970. After retiring Enrique has served as club president for Club Necaxa and of the Federacion Mexicana de Futbol Asociacion. He was a commentator for Univision at the FIFA World Cup Germany 2006 tournament. In 2007 Borja became club president for Tigres UANL.