He played college football at Southern Methodist University (SMU) and was selected in the sixth round of the 2011 NFL draft by the Washington Redskins.

He also played for the Baltimore Ravens, Atlanta Falcons, San Francisco 49ers, Minnesota Vikings, and Carolina Panthers.

He was ranked 96th on The Dallas Morning News Area Top 100 list and named a Dave Campbell's Texas Football Player to Watch.

Robinson was named an honorable mention All-Conference USA player and to the Pegasus News All-DFW College Football Team.

[14] At the start of 2012 training camp, it was announced that Robinson was taking reps as a punt returner, providing competition for Brandon Banks.

[17] Robinson made his NFL debut in the 2012 season opener win against the New Orleans Saints, subbing in for Pierre Garçon, who missed the entire second half of the game after suffering a foot injury.

[21] Though he recorded 40 yards on two receptions, he dropped a crucial 57-yard pass that hit him in the chest in the fourth quarter in their 31–28 loss to the Rams.

[27] After having a quiet start to the 2013 season, Robinson caught two passes for 75 yards, which included a 45-yard touchdown reception from Robert Griffin III in the 45–41 Week 7 win against the Chicago Bears.

[32] On April 2, 2014, Robinson announced that he would be switching over to #15, allowing new teammate DeSean Jackson to wear number 11.

[44] In Week 4 of the 2018 season, against the Los Angeles Rams, he recorded two receiving touchdowns from Kirk Cousins in the 38–31 loss.

[48] In February 2022, Robinson became an offensive assistant on head coach Mike McDaniel’s inaugural staff with the Miami Dolphins.