Carson played two seasons for Butler Community College in El Dorado, Kansas, east of Wichita, then transferred to Oklahoma State in 2015 and played two seasons under head coach Mike Gundy. As a junior in 2015, he had 17 carries for 104 rushing yards and two rushing touchdowns against UTSA; for the season, he had 517 rushing yards, four rushing touchdowns, and 17 receptions for 170 receiving yards. On November 19, 2016, against TCU, he had 17 carries for 146 yards and a touchdown. Overall, he finished the 2016 season with 559 rushing yards, nine rushing touchdowns, 13 receptions, 128 receiving yards, and a receiving touchdown.

In the 2017 NFL Draft, Carson was selected by the Seattle Seahawks in the seventh round, 249th overall. Two weeks later on May 12, the Seahawks signed him to a four-year, $2.46 million contract with a signing bonus of $65,129.

In his NFL debut on September 10, 2017, Carson had six rushes for 39 yards and one reception for ten yards in a 17–9 loss to the Green Bay Packers. In Week 2, against the San Francisco 49ers, his role expanded with 20 carries for 93 yards. Carson emerged as the Seahawks main running back ahead of veterans Thomas Rawls and Eddie Lacy, starting Weeks 3 and 4. In Week 3, against the Tennessee Titans, he had his first career receiving touchdown on a ten-yard reception from Russell Wilson. However, in Week 4 against the Indianapolis Colts on Sunday Night Football, Carson was carted off with a significant ankle injury. The next day, it was revealed that Carson broke his ankle and was placed on injured reserve. Overall, he finished his rookie season with 208 rushing yards to go along with seven receptions for 59 receiving yards and a receiving touchdown.

Carson returned from his injury to contribute immediately for the Seahawks in the 2018 season. In Week 3, against the Dallas Cowboys, he had 32 carries for 102 rushing yards and a rushing touchdown to go along with two receptions for 22 receiving yards in the 24–13 victory. In Week 5, in the 33–31 loss to the Los Angeles Rams, he had 116 rushing yards. Carson went on to have a great second season finishing fifth in the NFL in rushing yards (1,151) and tied for seventh in the NFL with nine rushing touchdowns. Carson was the first Seahawks running back to rush for over 1,000 yards since Marshawn Lynch in 2014. The Seahawks as a whole, led the league in rushing behind Carson’s efforts leading the way. The Seahawks made the playoffs and faced off against the Dallas Cowboys in the Wild Card Round. Carson had 13 carries for 20 yards in his playoff debut, a 24–22 loss.

In Week 1 against the Cincinnati Bengals, Carson rushed 15 times for 46 yards and a touchdown and caught six passes for 35 yards and a touchdown in the 21–20 win. In Week 4, against the Arizona Cardinals, Carson had 145 scrimmage yards (104 rushing, 41 receiving) in the 27–10 victory. In Week 5 against the Los Angeles Rams, Carson rushed 27 times for 118 yards and caught a five-yard touchdown pass on a fourth down late in the game during the 30–29 win. In Week 6 against the Cleveland Browns, Carson rushed 24 times for 124 yards and a touchdown and caught four passes for 35 yards in the 32–28 win. In Week 10 against the San Francisco 49ers on Monday Night Football, Carson rushed 25 times for 89 yards and a touchdown in the 27–24 overtime win. In Week 13 against the Minnesota Vikings on Monday Night Football, Carson rushed 23 times for 102 yards and a touchdown during the 37–30 win. During Week 15 against the Carolina Panthers, Carson finished with 133 rushing yards and two touchdowns as the Seahawks won 30–24. In Week 16, Carson suffered a fractured hip and was placed on injured reserve on December 24, 2019, ending his season. Carson finished the 2019 season with 1,230 rushing yards and seven rushing touchdowns to go along with 37 receptions for 266 receiving yards and two receiving touchdowns.

Carson was named to the Pro Bowl on January 17, 2020 as an alternate.