Brackens attended the University of Texas at Austin, where he played for the Texas Longhorns football team from 1992 to 1995. He developed a reputation as a ferocious hitter as a defensive end. As senior in 1995, he was recognized as a consensus first-team All-American and was also a first-team All-Southwest Conference selection. He finished his career ranked eighth on the Longhorns' all-time list with 24 sacks. He was also a key contributor to the 1995 Longhorns team that went 10-1 and won the Southwest Conference and gained a berth in the 1996 Sugar Bowl against the Virginia Tech Hokies.
He was taken in the second round of the 1996 NFL draft by the Jacksonville Jaguars, for whom he played his entire professional career. His lone Pro Bowl appearance came in 2000, after the 1999 season in which he had 12 sacks and 8 forced fumbles. As of 2011, he held the all-time Jacksonville Jaguars records for several categories: sacks (55), fumble recoveries (13) and forced fumbles (28). He is also the leading tackler (all-time) among Jaguars defensive ends.
He was released in 2004, after a series of troubling leg injuries and operations. About his release, Brackens stated, "Mentally and physically, I thought I could probably still do it, but I didn’t want to put up with all the rule changes. All the stuff they’re doing to players takes the fun out of the game." The moment in which he was let go was captured by NFL Films in "Jacksonville Jaguars: Inside the Training Camp", an unofficial version of the Hard Knocks TV series.