Robinson attended South Miami High School before attending Gulliver Preparatory School. He played both defensive back and wide receiver. As a senior he had 11 interceptions on defense and ten touchdowns on offense. As a junior he had 32 receptions for 491 yards and six touchdowns on offense and eight interceptions on defense.
Considered a four-star recruit by Rivals.com, Robinson was listed as the No. 16 cornerback prospect in the nation. He chose Florida State over Florida and Minnesota.
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.