After going a combined 8-6 with a 2.62 earned run average (ERA) on the three Yankee farm teams, Aceves was called up to the Yankees on August 28, 2008. On August 31, Aceves made his Yankee and major league debut, pitching two scoreless innings in relief.
Aceves married his wife Arley in November 2008, after proposing to her during a Trenton Thunder game during the 2008 season. His father, Alfredo Aceves Sr., was a first baseman in the Mexican League. His older brother, Jonathan Aceves, was a minor league catcher in the Chicago White Sox organization, for the Naranjeros de Hermosillo in the Mexican Pacific League and for the Saraperos de Saltillo of the Mexican League. Aceves wears #91, a number worn by Dennis Rodman, whom Aceves admires. Aceves' son Apollo was born on August 1, 2013.