Dickerson's family moved to Pearland in 1957, but it was not until after integration that he attended Pearland schools. Before the third grade he attended Ralph A Bunch in Manvel, Texas. In high school, he was a three-year starter at running back and also played linebacker. He received All-American honors as a senior.
He began his college career at Henderson County Junior College, where he was a Junior College All-American and All-conference linebacker from 1975 to 1976.
Dickerson moved on to Southern Methodist University where he was named captain and a starter at linebacker, finishing with 136 tackles (62 solo), one safety, one caused fumble, and one blocked kick. He also had a game against Ohio State University where he recorded 32 tackles. In 1978, he was let go by head coach Ron Meyer.
On October 1, 2011, he was inducted to the Trinity Valley Community College Cardinal Hall of Fame.
In 1978, he signed with the Toronto Argonauts of the Canadian Football League. He was waived on October 3.
In 1978, he signed with the Calgary Stampeders of the Canadian Football League and played in two games before being released.
After being cut by the Calgary Stampeders he moved to Los Angeles and got a job as a maintenance department stock clerk at the Burbank Airport. He was taking business courses at the University of Houston when the Dallas Cowboys signed him as an undrafted free agent in 1980. He made the team because he was one of the fastest linebackers in the NFL and contributed during his first years on special teams and in the nickel defense, replacing linebacker D. D. Lewis on passing downs. He posted 2 interceptions, 6 passes defensed, 3 forced fumbles (tied for the team lead) and one fumble recovery. He was named the Cowboys special teams player of the year after the season.
In 1981, he was named special teams captain and repeated as the Cowboys special teams player of the year. He also played on the nickel defense, registering 4 sacks and 2 fumble recoveries. The next year he had 2.5 sacks and one interception.
In 1983, he was named the starter at right outside linebacker after Guy Brown retired. He finished with 114 tackles (second on the team), 6 passes defensed, 2 forced fumbles, 3 fumble recoveries, one interception and 10.5 sacks (second on the team), the most ever by a linebacker in franchise history (it was broken by DeMarcus Ware in 2006).
Dickerson entered the 1984 season as a rising star, but the team decided to alternate him with first round draft choice Billy Cannon Jr. and his production dropped to 2 sacks and one interception. The next year, he was traded to the Buffalo Bills in exchange for a seventh-round draft selection in the 1986 NFL Draft.
In 1985, he played mainly on special teams and did not start any games. He was released on August 11, 1986.
On August 14, 1985, he signed as a free agent with the Miami Dolphins, who were having health problems with their outside linebackers. He was cut on August 19.