Selected by the Houston Astros in the 30th round (790th overall) of the 1990 Major League Baseball Draft, Singleton opted to attend the University of Nevada. His stock rose considerably over the next three years, and he was selected by the San Francisco Giants in the 2nd round (48th overall) of the 1993 Major League Baseball Draft. On November 11, , he was traded by the Giants with pitcher Alberto Castillo to the New York Yankees for Charlie Hayes and cash. On December 8, 1998, the Yankees dealt him to the White Sox for minor leaguer Rich Pratt.