After college, Griffith had a brief stint in the Canadian Football League playing for the Gold Miners. Soon after, Griffith had the opportunity to play in the NFL and joined the Minnesota Vikings. In his first two seasons, he was mostly used as a backup and as a special teams player before having a breakthrough year in the 1996 season. That season, he made four interceptions for 66 yards, and made 96 tackles. He was named All-Pro by Pro Football Weekly, and was second team Associated Press All-Pro in the 1998 season after having a career-high of five interceptions, finishing fifth in the NFC. He made the Pro Bowl after the 2000 season after starting in all 16 games, making one interception and 104 tackles. Griffith broke their long-standing special team record for 29 tackles. After eight seasons with the Vikings, Griffth signed a free agent contract with the Browns during the 2002 offseason, where he became one of the most experienced members in a young defense. He started in 44 games with the Browns earning six interceptions and 408 tackles in his three seasons. He led them in tackles with 118 in the 2004 season. He was released on February 27, 2005 as a cap casualty by then recently hired head coach, Romeo Crennel, who was trying to rebuild the franchise following a 4-12 season. He then signed a two-year contract with the Cardinals, where he started his last season and was active in all 16 games, making 79 tackles and three interceptions for 30 yards. In 2008, he signed a contract to retire as a member of the Minnesota Vikings. Robert was also a three-time All-Madden Selection, earned the 1999 Ed Block Courage and NFLPA Unsung Hero Awards, NFL Special Effort Awards and the 2000 Minnesota Man of the Year Award.