Straw made his professional debut with theGreeneville Astros, with whom he batted .268 with 22 stolen bases in 58 games. He played in 2016 with theQuad Cities River Bandits andLancaster JetHawks,slashing a combined .358/.423/.454 with one home run, 27 RBIs, and 21 stolen bases in 87 total games, and 2017 with theBuies Creek Astros andCorpus Christi Hooks[3] where he hit a combined .290 with one home run, 44 RBIs, and 38 stolen bases in 127 games.[4] Straw started 2018 with Corpus Christi and was promoted to theFresno Grizzlies during the season.[5][6]
Straw was promoted to the major leagues on September 15,2018. He scored his first career run on September 21, 2018, off of a bunt byJake Marisnick. He was a pinch runner forJ. D. Davis. The next day, Straw recorded his first career steal. On September 29, 2018, Straw hit his first Major League home run, against starting pitcherYefry Ramírez of theBaltimore Orioles.[7]
In2019, Straw batted .269/.378/.343 with 27 runs, 7 RBIs, and 8 stolen bases while being caught once, in 108 at bats.[8]
In2020, Straw batted .207/.244/.256 with 8 runs, 8 RBIs, and 6 stolen bases while being caught twice, in 82 at bats. He played 27 games in center field, and one game at shortstop.[9]
On July 30, 2021, Straw was traded to theCleveland Indians in exchange for relieverPhil Maton and minor leaguerYainer Díaz.[10] Straw finished the 2021 season batting .271/.349/.348 with four home runs, 48 RBI and 30 stolen bases between the Astros and Indians.
On April 9,2022, Straw signed a 5-year, $25 million extension with the Guardians.[11] In 2022 he had the lowest slugging percentage and the lowest OPS (.564) in the majors, the lowest barrel percentage (0.7%), and the highest percentage of balls hit to the opposite field (36.1%).[12][13] He batted .221/.291/.273 in 535 at bats, with no home runs, 32 RBI, and 21 stolen bases in 22 attempts.[14] On defense, he won aGold Glove Award in center field.[15]
On August 11, 2023, Straw hit a solo home run off ofTampa Bay Rays relieverJason Adam, his first homer since 2021.[16] In 2023, he batted .238/.301/.297, with one home run and a league-leading six sacrifice hits, had the lowest percentage of hard-hit balls of all AL players (18.0%), and had the lowest barrel percentage (0.5%).[17][18]
On March 22, 2024, Straw was placed on outright waivers.[19][20] After clearing waivers, Straw was sent outright to the Triple–AColumbus Clippers on March 24.[21][22] In 123 games for Columbus, he slashed .240/.321/.330 with three home runs, 47 RBI, and 30 stolen bases. On September 17, the Guardians selected Straw's contract, adding him to their active roster.[23] In 7 games for Cleveland, he went 1–for–4 (.250) with 2 stolen bases. On November 1, Straw was removed from the 40–man roster and sent outright to Columbus.[24]
On January 17, 2025, the Guardians traded Straw, cash, and international signing pool space to theToronto Blue Jays in exchange for a player to be named later.[25][26] On March 27, the Blue Jays selected Straw's contract after he made the team'sOpening Day roster.[27]