Straw made his professional debut with the Greeneville Astros, with whom he batted .268 with 22 stolen bases in 58 games. He played in 2016 with the Quad Cities River Bandits and Lancaster JetHawks, slashing a combined .358/.423/.454 with one home run, 27 RBIs, and 21 stolen bases in 87 total games, and 2017 with the Buies Creek Astros and Corpus 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 the Fresno 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 by Jake Marisnick. He was a pinch runner for J. 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 pitcher Yefry Ramírez of the Baltimore 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 the Cleveland Indians in exchange for reliever Phil Maton and minor leaguer Yainer Díaz.[10] Straw finished the 2021 season batting .271/.349/.348 with 4 home runs, 48 RBIs 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 zero home runs, 32 RBIs, and 21 stolen bases in 22 attempts.[14] On defense, he won a Gold Glove Award in center field.[15]
On August 11, 2023, Straw hit a solo home run off of Tampa Bay Rays reliever Jason 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] After clearing waivers, Straw was sent outright to the Triple-A Columbus Clippers on March 24.[20]
