Cajuste played college football for West Virginia. He redshirted during the 2014 season. During the 2015 season, he started 6 games before suffering an injury against Baylor. He would return at the end of the season however, as the Mountaineers won the Cactus Bowl. In 2016, he sustained a season-ending injury during the first game of the season against Missouri. During 2017, he started 13 games for the Mountaineers and earned All-Big 12 Conference Second Team honors. During his final season, 2018, he earned multiple honors including Football Writers Association of AmericaAll-American (Second Team), Phil Steele All-America (Second Team), Athlon Sports All-America (Fourth Team), Big 12 Conference Co-Offensive Lineman of the Year, and All-Big 12 Conference First Team.
Cajuste was drafted by the New England Patriots in the third round (101st overall) of the 2019 NFL Draft.[3] He was placed on the non-football injury list to start the season after undergoing quad surgery.
On September 10, 2020, Cajuste was placed on injured reserve with a knee injury.[4]
Cajuste entered the 2021 season as a backup tackle for the Patriots. He made his first career starts in Weeks 5 and 6 at right tackle.
On October 1, 2022, Cajuste was placed on injured reserve with a thumb injury.[5] He was activated on October 29.[6]
On May 18, 2023, Cajuste was waived by New England.[7]
New York Jets
On May 30, 2023, Cajuste signed with the New York Jets.[8] He was waived/injured on August 8, 2023.[9] After going unclaimed, he reverted to the team’s injured reserve list.[10] He was released on August 17.
New York Giants
On October 11, 2023, Cajuste signed with the practice squad of the New York Giants.[11] Following the end of the 2023 regular season, the Giants signed him to a reserve/future contract on January 8, 2024.[12]