White spent his first professional season with the Arizona League Athletics and Vermont Lake Monsters, hitting .275 with two home runs and 25 RBIs in 56 games.[8][9] He played for the Stockton Ports in 2017, hitting .270 with four home runs and 36 RBIs in 115 games.[9] In 2018, he played for the Midland RockHounds,[10] slashing .306/.388/.450 with nine home runs, 55 RBIs, and 18 stolen bases in 130 games.[9][11] After the 2018 season, he played in the Arizona Fall League for the Mesa Solar Sox.[12]
On December 21, 2018, the Rangers acquired White from the Athletics as part of a three-team deal in which the Rangers also acquired Kyle Bird, Brock Burke, Yoel Espinal, and $750,000 of international signing bonus pool space, the Rays acquired Emilio Pagán, Rollie Lacy, and a competitive balance pick in the 2019 MLB draft, and the Athletics acquired Jurickson Profar.[13]
In 2019, White played for the Nashville Sounds of the Triple-A Pacific Coast League.[14] White's season ended early on August 20, when he suffered a shoulder injury after crashing into an outfield wall.[15] White produced a .253/.320/.418/.738 slash line with 14 home runs and 43 RBI over 116 games in 2019.[16][9]
On September 1, 2020, White made his MLB debut against the Houston Astros.[17] Over 19 games with Texas in 2020, White hit .188 with 3 RBI.
On June 16, 2021, White hit his first and second career home runs, the first one off of Houston Astros starting pitcher Zack Greinke, and the second off of Astros starter-turn reliever Cristian Javier.[18] He spent 20 games with the Round Rock Express of the Triple-A West in 2021, hitting .343/.450/.537/.987 with 3 home runs and 11 RBIs.
In 64 games with Texas in 2021, he hit .177/.259/.308/.567 with 6 home runs and 15 RBIs. In 2021, he had the fastest sprint speed of all major league left fielders, at 30.5 feet/second.[19] He underwent Internal Brace surgery on his right elbow on September 8, 2021.[20] Over 47 games for Texas in 2022, White hit just .200/.274/.305/.578 with 3 home runs, 10 RBI, and 12 stolen bases. He underwent surgery in June 2022 due to suffering a right wrist fracture and missed the remainder of the season.[21]
On December 23, 2022, White was designated for assignment.[22]
On December 28, 2022, White was traded to the Atlanta Braves in exchange for cash considerations.[23] White was optioned to the Triple-A Gwinnett Stripers to begin the 2023 season.[24] White made only 6 appearances for the Braves, going 1–for–14 (.071) with 2 walks. On July 18, 2023, White was shut down for the remainder of the season after suffering a torn labrum in his left shoulder.[25] On July 22, he was released by the Braves following the promotion of Allan Winans.[26] On July 25, White re–signed with the Braves on a minor league contract.[27]
White began the 2024 season with Triple–A Gwinnett, hitting .294/.402/.462 with seven home runs, 28 RBI, and 18 stolen bases across 53 games. On July 5, 2024, the Braves selected White's contract, adding him to the major league roster.[28]