Robinson attended Florida State University from 2006 to 2009. As a freshman in 2006, he played in 12 of 13 games and recording 11 tackles. He also blocked a PAT attempt that was returned for a touchdown by Tony Carter, making it first time in school history blocked PAT had been returned for a touchdown. As a sophomore in 2007 he started five of 12 games, recording 27 tackles and a team leading six interceptions. During the season he set the school record for consecutive games with an interception with five. As a junior in 2008 he started eight of 13 games, recording 26 tackles and one interception. As a senior in 2009 he recorded 46 tackles.
Robinson and the Saints agreed to a five-year contract on July 29, 2010. On November 5, 2012, Robinson intercepted a pass from Michael Vick of the Philadelphia Eagles and returned it 99 yards for a touchdown, tying a Saints record set by retired safety Darren Sharper.