A native of Columbia, South Carolina, Roberts attended Spring Valley High School, where he was a two-sport star in football and track. He earned All-region and All-area honors as a senior and led the Vikings to the regional championship and state semi-finals. He earned MVP honors for his performance in the 2005 North-South All-Star game.
In addition to football, Roberts lettered in track & field while at Spring Valley, leading his team to the state championship in 2003 and a second-place finish as a senior, the season he captured All-State recognition. He posted personal-bests of 11.2 in the 100-meter dash, 21.91 in the 200-meter dash and 48.60 in the 400-meter dash.
Roberts attended The Citadel, The Military College of South Carolina from 2006 to 2009, where he played football and ran track. During his career, he had 286 receptions for 3,743 yards and 36 touchdowns.
Roberts joined The Citadel outdoor track team in Mid-March, 2007, earning his first Penn Relays Championship watch. He made his debut at the Furman Invitational (4/07), as he finished third in the 400-meters, running 50.91. Also at Furman, he finished second in the 200-meters with a time of 23.49. He ran a collegiate-best 200-meter time of 23.05 at the Chanticleer Invitational (4/14). He ran the anchor leg of the 4x100-meter relay that clocked 41.94 at the Southern Conference Champion-ships (4/22), garnering All-Conference honors. Also ran the anchor leg of the 4x100-meter relay team that won at the Penn Relays for the fifth consecutive time in Citadel history. He graduated in three and a half years with a degree in accounting.
Roberts was drafted in the third round with the 88th overall pick by the Arizona Cardinals in the 2010 NFL Draft.
Roberts started out his rookie season playing limited time as a punt returner. As the season went on, Roberts started playing more snaps and started to move into the second receiver slot. He caught his first NFL touchdown against the Minnesota Vikings, a 27-24 loss in OT. He caught his second NFL touchdown, a 74-yard completion, on Christmas Day against the Dallas Cowboys, a game that was won in the last minute 27-26.
On March 11, 2014, Roberts and the Washington Redskins agreed to terms on a four-year contract, worth roughly $16 million. The contract was finalized the next day. Later that month, Roberts made a $12,000 donation to the Kirk Cousins Football Camp, allowing Roberts the rights to wear number 12, which he wore for four seasons in Arizona. He originally signed with the intention to be the Redskins' number two wide receiver, opposite of Pierre Garçon, but became the number three receiver after the signing of DeSean Jackson. He also became the team's new return specialist.
In the Week 4, 45-14 loss against the New York Giants, Roberts scored one of the only two Redskins' scores in the game after catching an 18-yard pass from Cousins. It was his first touchdown with the Redskins.
In Week 11 of the 2015 season, Roberts returned a kick 99 yards for a touchdown against the Carolina Panthers. On December 21, 2015, he was placed on injured reserve with an knee injury, ending his season.
Roberts was released by the Redskins on May 17, 2016.
On June 13, 2016 Roberts signed a one-year deal with the Detroit Lions.
On October 2, 2016, Roberts returned a punt 85 yards for a touchdown against the Chicago Bears.
On March 14, 2017, Roberts signed a one-year contract with the Atlanta Falcons.