Fulton appeared in three games as a freshman, making two tackles. Following the season, Fulton was suspended by the NCAA for two seasons after he tampered with a drug test for performance enhancing drugs on February 2, 2017.[6] He appealed the decision, arguing that he believed that the test was for recreational narcotics, but the initial appeal was denied in March 2017. Fulton sat out the entirety of the 2017 season, but remained with the team and participated in daily practices.[7] Fulton then filed a second appeal after hiring an attorney arguing that proper drug testing protocol was not followed.[8] The second appeal was also originally denied by a panel of NCAA officials on August 9, 2018, but the decision was overturned on August 23.[9][10]
Fulton entered his junior season as a starter at cornerback for the Tigers, despite not having played in a game in 18 months.[11] He started the first ten games of the season for LSU before suffering a season ending ankle injury against Arkansas and finished the season with 25 tackles (one for loss), an interception, and nine passes defended.[12] Entering his senior season, Fulton was named a preseason All-American by the Associated Press and the third-best defensive back in the nation by USA Today.[13] He finished the season with 38 tackles, one interception and 14 passes defended as LSU won the 2020 National Championship.[14]
Fulton was selected by the Tennessee Titans with the 61st overall pick in the second round of the 2020 NFL draft.[17][18] He signed his four-year rookie contract on July 27, 2020.[19] Fulton made his NFL debut in the Titans season opener against the Denver Broncos, making four tackles.[20] In Week 2 against the Jacksonville Jaguars, Fulton recorded his first career interception off a pass thrown by Gardner Minshew and returned it for 44 yards during the 33–30 win.[21]
In Week 3 against the Minnesota Vikings, Fulton recorded his first career sack on Kirk Cousins during the 31–30 win.[22] He was placed on the reserve/COVID-19 list by the team on October 1, 2020,[23] and activated on October 13.[24] He was placed on injured reserve on October 31 with a knee injury.[25] He was activated off of injured reserve on December 15, 2020.[26]
Fulton entered the 2021 season as a starting cornerback for the Titans. He started the first five games before suffering a hamstring injury in Week 5. He was placed on injured reserve on October 18, 2021.[27] He was activated from injured reserve on November 13, 2021.[28]
Fulton entered the 2023 season as a starting cornerback. After dealing with a nagging hamstring injury throughout the season, he was placed on injured reserve on December 13, 2023.[29]