Aquino signed with the Toronto Blue Jays as an amateur free agent in 1981 and made his major league debut with Toronto in 1986. He was later traded to the Kansas City Royals for Juan Beníquez. Aquino played most of his professional career with the Royals, but also had major league appearances for the Marlins, Expos and Giants.
In a nine-year career, Aquino posted a 31–32 record with five saves and an ERA of 3.68, lower than the league average over his career.
Aquino was a member of the inaugural Florida Marlins team that began play in 1993.