Culver attended St. Martin de Porres High School in Detroit, Michigan and earned a scholarship to the University of Notre Dame, where he started as a tailback in 1990 and 1991.

The Irish backfield had a number of talented running backs, including future pros Ricky Watters and Reggie Brooks and NFL Hall-of-Famer Jerome Bettis.

Culver played as a freshman on the 1988 national-championship team, including a five-yard touchdown run in the 1989 Fiesta Bowl against West Virginia.

The following year, Culver was injured but played spectacularly in Notre Dame's 39–28 defeat of the University of Florida Gators.

Culver was the last man in a talented San Diego backfield that included newcomer Natrone Means and halfbacks Eric Bieniemy and Ronnie Harmon.

Culver scored the tying touchdown, the last of his career, in the infamous 1995 Chargers-Giants "Snowball Game" at Giants Stadium.