He played college football at Oklahoma State before transferring to Virginia for 2021, where he was named first-team All-ACC.

He joined the team as an early enrollee and redshirted his freshman year and was moved from quarterback to tight end during the Cowboys practices leading up to the 2017 Camping World Bowl.

[8] As a redshirt sophomore, he caught 16 passes for 112 yards and a touchdown and was an honorable mention All-Big 12 Conference selection.

[16][17] In Week 3, against the Kansas City Chiefs, Woods scored his first two professional touchdowns on his first two career receptions in a 20–17 victory.

[19] On August 23, 2024, it was announced that Woods had undergone toe surgery and would miss roughly four months in recovery.