Roberts began his career at Isthmian League First Division club Wembley and secured a £6,000 move to the Football League with Third Division club Brentford in 1980. He made 19 appearances and scored three goals in the 1980–81 season. Following the departure of David Crown, Roberts was a regular during the following season, playing as a left winger, despite being right-footed. He also served as the club's PFA representative. Roberts came to the fore during the 1982–83 season, scoring 17 goals and amassing a career-high 58 appearances. He followed up with another 15 goals in 1983–84 and won the Midweek Sports SpecialGoal of the Month award for his finish in a 4–1 League Cup second round first leg defeat to First Division club Liverpool. Roberts continued to find the net during the 1984–85 season, scoring a hat-trick against Gillingham and scoring four in the 6–0 rout of Newport County in the Football League Trophy Southern Area final, which included a three-minute hat-trick either side of half time. Needing to raise transfer funds, Roberts was transfer-listed by manager Frank McLintock and he turned down a move to Bradford City. A move to fellow Third Division club Derby County prior to the start of the 1985–86 season was scuppered by an ankle injury. Roberts remained at Griffin Park and managed just three appearances during the season, before retiring from professional football at the end of the campaign due to the ankle injury. Roberts made 224 appearances and scored 63 goals during his six years with the Bees. He received a testimonial in May 1989, which raised £7,000 and was inducted into the Brentford Hall of Fame in February 2020.
Roberts again returned to one of his former clubs, St Albans City, to take over as assistant alongside manager Steve Cook in 2001. A mid-table finish followed in the 2001–02 season, bu the pair were sacked in December 2002, with the club top of the Isthmian LeaguePremier Division table.
Cambridge City
Roberts took over as manager of Cambridge City in January 2003. In what remained of the 2002–03 season, he managed to steer the club away from relegation from the Southern League Premier Division. An eighth-place finish followed in 2003–04, before a restructuring of the non-league pyramid in 2004 saw the Lilywhites playing in the newly formed Conference South for the 2004–05 season. Roberts led the club to a second-place finish, but the season ended in heartbreak after defeat to Eastbourne Borough in the playoff semi-finals. Roberts kept City in the Conference South for three further seasons, before suffering demotion back to the Southern League Premier Division in 2008, due to irregularities with the club's Milton Road ground. Over the following six seasons, Roberts guided City to five top-six finishes and a memorable run to the first round proper of the FA Cup in the 2012–13 season, taking League One club Milton Keynes Dons to a replay before being knocked out. He stepped down as manager at the end of the 2015–16 season.