Spencer accepted an athletic scholarship to attend the University of Florida in Gainesville, Florida, where he played for coach Galen Hall and coach Steve Spurrier's Gators teams from 1988 to 1990.
[3] In 1990, he blocked a punt late in the fourth quarter, which Richard Fain recovered and returned twenty-five yards for a touchdown and providing the margin of victory in the Gators' 17–13 victory over the Alabama Crimson Tide in Tuscaloosa, Alabama.
The Washington Redskins selected Spencer in the eighth round (215th pick overall) of the 1991 NFL draft.
[5] Spencer played for the New Orleans Saints from 1992 to 1995, the Cincinnati Bengals in 1996 and 1997, the San Diego Chargers in 1998 and 1999, and the Denver Broncos from 2000 to 2003.
[1] In 2003, Spencer worked as an assistant defensive back coach with the Broncos in addition to playing, making him the first simultaneous player/coach in the NFL since Dan Reeves in 1972.