Thompson officially signed with the Rangers a few days after the draft[12] and was assigned to the AZL Rangers, where he spent the whole season, posting a .257 batting average in 113 at bats with three home runs and 12 RBIs in thirty games.[13] He spent 2018 with the Hickory Crawdads of the Single–ASouth Atlantic League, where he slashed .289/.344/.446 in 332 at bats with eight home runs, 42 RBIs, and 32 stolen bases in 39 attempts.[14]
Thompson was ranked as the #48 overall prospect in baseball by Baseball Prospectus in their preseason 2019 Top 101 list.[15] He was ranked as the #108 overall prospect in baseball by Fangraphs in their preseason 2019 Top 130 list.[16]
Thompson was assigned to the Down East Wood Ducks of the High–ACarolina League for the 2019 season.[17][18] He was placed on the injured list on April 17, after suffering a fractured hamate bone in his left hand.[19] He finished an injury-marred season hitting .178/.261/.312/.573 in 202 at bats with five home runs and 21 RBIs and 12 steals in 15 attempts in 57 games.[20] Thompson played in the Arizona Fall League for the Surprise Saguaros following the 2019 season,[21][22] and was named a Fall League All-Star.[23]
Thompson did not play in 2020 due to the cancellation of the Minor League Baseball season due to the COVID-19 pandemic. Thompson spent the 2021 season with the Frisco RoughRiders of the Double-A Central, hitting .275/.325/.483 in 429 at bats with 16 home runs, 52 RBIs, and 25 stolen bases in 33 attempts.[24][25] He was named the co-winner of the Rangers' 2021 True Ranger Award, along with Keyber Rodriguez.[26] Thompson opened the 2022 season with the Round Rock Express of the Triple-APacific Coast League, hitting .304/.355/.474 in 346 at bats with 13 home runs, 48 RBIs, and 49 stolen bases (a Round Rock record, and second in the PCL) in 52 attempts over 80 games.[27][28][29][30]
On August 4, 2022, Texas selected Thompson's contract and promoted him to the active roster to make his MLB debut versus the Chicago White Sox.[31] In his debut, Thompson recorded his first career hit, a bunt single off of Johnny Cueto.[32] On August 30, Thompson hit his first career home run, a solo shot off of Houston Astros starter Framber Valdez.[33] In 2022 with Texas, he batted .265/.302/.312 in 170 at bats with 18 steals in 21 attempts, and his 85.71% stolen base percentage was 8th-best in the American League, as he played primarily left field.[34] He had the second-fastest sprint speed of all major league batters, at 30.4 feet/second.[35]
In 37 games for Texas in 2023, Thompson batted .170/.237/.283 with 4 RBI and 4 stolen bases. On August 11, 2023, Thompson was designated for assignment following the promotion of J. P. Martínez.[36]
Kansas City Royals
On August 13, 2023, Thompson was claimed off waivers by the Kansas City Royals.[37] In 33 games for the Triple–A Omaha Storm Chasers, Thompson hit .259/.313/.410 with 4 home runs, 17 RBI, and 11 stolen bases.
Cincinnati Reds
On October 26, 2023, Thompson was claimed off waivers by the Cincinnati Reds,[38] who designated him for assignment on December 28.[39] He was then claimed by the New York Yankees on January 4, 2024[40] designated for assignment on January 19,[41] and claimed by the Minnesota Twins on January 24.[42] Thompson was designated for assignment by the Twins on February 7 following multiple waiver claims,[43] and was then claimed again by the Reds on February 13.[44] Thompson was optioned to the Triple–A Louisville Bats to begin the 2024 season.[45] On March 27, Thompson was recalled from Louisville.[46] He played in 17 games for Cincinnati, but went 2–for–18 (.111) with no home run or RBI. On May 23, Thompson was designated for assignment by the Reds.[47] He cleared waivers and was sent outright to the Double–A Chattanooga Lookouts on May 25.[48]