After signing, Alexy was assigned to the
Arizona League Dodgers to make his professional debut; in 13+2⁄3 innings pitched for them, he posted a 1–0 record and a 4.61 ERA. He began the 2017 season with the
Great Lakes Loons.[5]
Texas Rangers
On July 31, 2017, the Dodgers traded Alexy, along with
Willie Calhoun and
Brendon Davis, to the
Texas Rangers in exchange for
Yu Darvish.[6][7] The Rangers assigned him to the
Hickory Crawdads, where he finished the season. In 19 starts for Great Lakes he was 2–6 with a 3.97 ERA, striking out 86 in 73+2⁄3 innings, and in five starts for Hickory he was 1–1 with a 3.05 ERA.[8][9] He spent 2018 with Hickory, going 6–8 with a 3.58 ERA and 138 strikeouts over 108 innings.[10][9] Alexy was assigned to the
Down East Wood Ducks of the
High–ACarolina League for the 2019 season,[11] going 0–3 with a 5.12 ERA in 19+1⁄3 innings. He suffered a strained
Latissimus dorsi muscle in his back during a game on May 1 and received a
PRP injection as part of his rehab process.[12] Alexy missed the rest of the 2019 season due to the lat injury.[13] Following the 2019 season, Alexy played for the
Surprise Saguaros of the
Arizona Fall League.[14] Alexy did not play in a game in 2020 due to the cancellation of the Minor League Baseball season because of the
COVID-19 pandemic.
On November 20, 2020, Alexy was added to the Rangers 40-man roster.[15] Alexy opened the 2021 season with the
Frisco RoughRiders of the
Double-A Central league.[16] After going 3–1 with a 1.61 ERA and 57 strikeouts over 50+1⁄3 innings for Frisco, he was promoted to the
Round Rock Express of the
Triple-A West on August 3.[17][18]
On August 30, 2021, Alexy was promoted to the active roster to make his MLB debut that night versus the
Colorado Rockies.[19] In his debut, he recorded the win while throwing five scoreless innings with four strikeouts.[20][21] Over five games for Texas in 2021, Alexy posted a 3–1 record with a 4.70 ERA and 17 strikeouts over 23 innings.[22] With Round Rock in 2022, he went 6–6 with a 5.91 ERA over 96 innings. With Texas, he went 1–1 with a 11.57 ERA over 7 innings.[23]
The Rangers
designated Alexy for assignment on December 9, 2022.[24]
Chicago White Sox
On December 13, 2022, Alexy was claimed off waivers by the
Washington Nationals.[23] Alexy was designated for assignment on January 4, 2023, after the signing of
Dominic Smith was made official.[25]
On January 10, 2023, Alexy was traded to the
Minnesota Twins in exchange for minor league right-hander Cristian Jimenez.[26] On January 23, Alexy was designated for assignment by Minnesota following the acquisition of
Michael A. Taylor.[27]
On January 30, 2023, Alexy was claimed off waivers by the
Chicago White Sox.[28] Alexy was optioned to the Triple-A
Charlotte Knights to begin the 2023 season.[29] Alexy struggled to an ugly 15.30 ERA and 10:18 K:BB in 4 appearances with Charlotte. On April 28, Alexy was removed from the 40-man roster and sent outright to Triple-A.[30] He was released on July 1, after remaining struggles left him at an 0–3 record and 12.00 ERA.[31]