Bojorquez signed with the New England Patriots as an undrafted free agent on May 14, 2018.[7] He was waived on September 1, 2018.[8] Bojorquez was one of the final preseason cuts by New England as the team opted to keep incumbent punter Ryan Allen, but was intended to be signed to their practice squad. He never played a snap during the preseason, only practicing some punts during the intermission of the last preseason game with the Patriots.[3]
Buffalo Bills
On September 2, 2018, Bojorquez was claimed off waivers by the Buffalo Bills, and was named the starting punter after the team released Colton Schmidt.[9] He made his NFL debut in the Bills' season opener against the Baltimore Ravens. In the 47–3 loss, he had eight punts for 397 net yards for a 49.6 average.[10] Bojorquez sustained a shoulder injury during the October 7 game against the Tennessee Titans; after playing three games with the injured shoulder, he was placed on injured reserve on October 31, ending his season.[11] Overall, he finished his rookie season with 45 punts for 2,028 net yards for a 45.07 average.[12]
In the 2019 season, Bojorquez finished with 79 punts for 3,313 net yards for a 41.94 average.[13] In the Wild Card Round of the playoffs against the Houston Texans, he was involved in an unusual sequence toward the end of the game. Bojorquez was normally the holder for the Bills on field goal attempts in 2019.[14] The Bills did not know if they had a first down or if they were short with little time remaining. The spot of the ball was being reviewed by the booth. If the spot remained a fourth down, the Bills would be forced to attempt a field goal with time expiring. To counter this, Bills' head coach Sean McDermott sent the special teams onto the field during the review. After the review, the Bills had earned a first down and the clock restarted. Instead of losing valuable time to get the special teams off of the field, Bojorquez had to get under center and spike the ball to stop the clock.[15]
In week 5 of the 2020 season against the Titans, Bojorquez had a career-long 74-yard punt, breaking his previous career long set the previous week.[16] In the 2020 season, he punted 41 times for a 50.78 average.[17]
On August 31, 2021, Bojorquez was traded to the Green Bay Packers along with a 2023 seventh-round draft pick in exchange for a 2023 sixth-round draft pick.[19]
On October 17, 2021, Bojorquez had an 82-yard punt in the third quarter of a 24–14 victory over the Chicago Bears. The punt was a new career long for Bojorquez, the second-longest in Packers history, and the longest of the 2021 NFL season.[20][21] In the 2021 season, he punted 53 times for a 46.55 average.[22]
Cleveland Browns
On April 4, 2022, Bojorquez signed with the Cleveland Browns.[23] He was named the starting punter in 2022, beating out Joseph Charlton. In Week 17, Bojorquez had four punts, two landing inside the 20-yard line with a long of 64 yards in a 24–10 win over the Washington Commanders, earning AFC Special Teams Player of the Week.[24] In the 2022 season, he punted 61 times with a 48.51 average.[25]
On March 15, 2024, Bojorquez signed a two-year contract extension with the Browns.[26]
Bojorquez is the oldest of four siblings, and is married to Diana Wong of Hilo, Hawaii.[3] He is an ordained minister.[27][28] He is of Mexican descent.[29]