He played college football for the North Carolina Tar Heels, and was selected by the St. Louis Rams with the 14th pick in the first round of the 2011 NFL draft.

[8] As a junior in 2010, Quinn missed the season after he was ruled ineligible by the NCAA for lying to investigators about receiving travel accommodations and jewelry.

[18] Throughout training camp, Quinn competed to be a starting defensive end against long time veteran James Hall.

[19] Head coach Steve Spagnuolo named Quinn the primary backup defensive end to start the season, behind veterans Chris Long and James Hall.

[21] On October 30, 2011, he recorded his second sack and blocked a punt against the New Orleans Saints, earning the NFC Special Teams Player of the Week Award for his effort.

[24] Quinn completed his rookie season with 23 combined tackles (20 solo), five sacks, three blocked punts, two pass deflections, and a forced fumble in 16 games and one start.

[25] On January 2, 2012, the St. Louis Rams fired head coach Steve Spagnuolo after they completed the season with a 4–12 record.

[27] Head coach Jeff Fisher named Quinn and Chris Long the starting defensive ends to begin the regular season.

On October 4, 2012, Quinn recorded six combined tackles (four solo) and a season-high three sacks on Kevin Kolb during a 17–3 win against the Arizona Cardinals.

[42] Due to injury, he appeared in eight games and finished with five sacks, 21 total tackles, three passes defensed, and three forced fumbles.

[46] In the 2017 season, Quinn finished with 8.5 sacks, 32 total tackles (21 solo), one pass defensed, and two forced fumbles in 15 games.

[56] In week 7 against the Philadelphia Eagles, Quinn recorded a sack on Carson Wentz before leaving the game with a rib injury.

[57] He finished the season with 25 tackles, 11.5 sacks (led the team), 37 quarterback pressures, three passes defensed and two forced fumbles.

[62] In Week 7 against his former team, the Los Angeles Rams, on Monday Night Football, Quinn forced a fumble on former teammate Robert Woods which was returned for a touchdown by Eddie Jackson during the 24–10 loss.

[70] Quinn was traded to the Philadelphia Eagles in exchange for a fourth round selection in the 2023 NFL draft on October 26, 2022.

[71] Two days later, Quinn and the Eagles mutually agreed to void the final two years of his contract, making him eligible for free agency following the season.

[76] On August 18, 2023, Quinn was arrested in Summerville, South Carolina and charged with seven counts including assault and battery and hit and run.

[77] On January 10, 2025, Quinn was arrested in North Charleston, South Carolina on charges of leaving the scene of an accident, which included property damage and reckless driving, following a car crash that involved multiple vehicles.