Acosta emigrated with his family to Los Angeles, California, in the United States of America, from Mexico[1] after 1910, to escape the violence[2] created by the Mexican Revolution.

Some of his extended family resided in Playa del Rey, California—including his adult son, Joaquín Enrique Acosta Sr., and daughter in law, Catalina Ortiz Acosta, a pianist working with Juanita Roos,[5][6] wife of Charles Roos[7] in the Indianist Movement.

Declaring themselves to be white on birth certificates and other public documents was common practice for many Mexican Americans in Los Angeles County during the 20th century.

Enrique Acosta worked with many early 20th Century film stars including Laurel and Hardy in many of Hal Roach Studio's Spanish-language shorts.

[3][19] At age 66, he played General Calixto García[20] in A Message to Garcia (1936), starring a very young Barbara Stanwyck.