He played college football for the New Mexico State Aggies and was signed by the Arizona Cardinals as an undrafted free agent after the 2002 NFL draft.

He completed his bachelor's degree in individualized studies (health science) in August 2008, while playing in the NFL for the San Francisco 49ers.

In 2003, Wragge was placed on the Cardinals' practice squad and suffered a season-ending knee injury that landed him on the injured reserved list for the rest of the 2003 season.

In 2004, Wragge attended training camp again with the Arizona Cardinals under the new head coach Dennis Green; he was released before the start of the 2004 regular season.

Wragge was named offensive line coach for the NFLPA Collegiate Bowl Game held on January 19, 2013.