Márquez played during one season at the major league level for the Chicago White Sox. He was purchased by the Los Angeles Dodgers from the Mexican League's Tuneros de San Luis in 1988. Márquez played his first professional season (in American baseball) with their Class A-Advanced Bakersfield Dodgers in 1988, and his last affiliated season with the White Sox and their Triple-A Nashville Sounds in 1995.
In 2000, he made a comeback with the Piratas de Campeche of the Mexican League. He pitched in Mexico through 2011.