Independent leagues Martin was not selected in the
2006 MLB draft. After graduating from McLennan, Martin signed with the
Fort Worth Cats of the
United League Baseball, which is
independent of MLB, for the 2007 season. Though Martin made the team out of their tryout camp, he did not pitch in a game for the Cats due to discomfort in his shoulder. A doctor recommended Martin undergo surgery to repair the labrum and the
articular capsule of the humerus. Martin and Jordan Bostick, a coworker in the warehouse and a former high school baseball teammate, began playing
catch in the warehouse. Martin noticed that his shoulder felt stronger, and with encouragement from Bostick, he agreed to attempt to play professional baseball again. In 2010, after three years out of baseball, Martin tried out with the
Grand Prairie AirHogs of the independent
American Association of Independent Professional Baseball. Martin threw
fastballs at before he was pulled aside by
Pete Incaviglia, the AirHogs
manager, and signed to a contract. He made his debut for the AirHogs that night. He had a 4–0
win–loss record and a 1.96
earned run average (ERA) for the AirHogs. The Red Sox assigned Martin to the
Greenville Drive of the
Single-A South Atlantic League to begin the 2011 season. Later in the year, the Red Sox promoted Martin to the
Salem Red Sox of the
High-A Carolina League and then the
Portland Sea Dogs of the
Double-A Eastern League. Across the three levels, Martin had a 6–2 win–loss record and 2.55 ERA in 23 appearances. but was moved back to a
relief role later in the season. He ended the 2012 season with a 4.48 ERA. In 2013, Martin worked exclusively in relief. He had a 5–3 win–loss record with a 2.25 ERA and five
saves in 42 games pitched, split between Portland and the
Pawtucket Red Sox of the
Triple-A International League during the 2013 season. The Rockies insisted on Martin's inclusion in the trade. The Rockies promoted Martin to the major leagues for the first time on April 25, 2014. before the Rockies demoted Martin to Colorado Springs in June. During the 2014–15 offseason, the Rockies agreed to sign
Nick Hundley. The Rockies
designated Martin for assignment on January 5, 2015, in order to remove him from their
40-man roster, so that the Rockies could sign Hundley.
New York Yankees The Rockies traded Martin to the
New York Yankees on January 13, 2015, receiving cash considerations. Martin competed for a spot in the Yankees' bullpen in spring training, and was named to the Yankees'
Opening Day roster. On April 28, 2015, Martin recorded his first career save in a 4–2 victory over the
Tampa Bay Rays. Martin began the season with a 0–1 record and a 3.55 ERA in innings pitched across 15 appearances, before he went on the
disabled list on May 9 due to
tendinitis in his right elbow. The Yankees activated Martin from the disabled list on May 31, and optioned him to the
Scranton/Wilkes-Barre RailRiders of the International League. The Yankees recalled Martin from the minor leagues on June 11 to fill in for the injured
Andrew Miller, and optioned him back to Scranton/Wilkes-Barre on June 19. He finished the 2015 season with a 0–2 record and a 5.66 ERA in 24 games pitched for the Yankees.
Hokkaido Nippon-Ham Fighters After the 2015 season, the Yankees sold the contractual rights to Martin to the
Hokkaido Nippon-Ham Fighters of
Nippon Professional Baseball's
Pacific League for $750,000. but injured his ankle in September. Martin missed the end of the regular season and the
2016 Japan Series, which the Fighters won. He finished the 2016 season with a 1.07 ERA and 21 saves. The Fighters re-signed Martin for the 2017 season for ¥100 million (approximately US$). He had a 1.19 ERA in 40 appearances with the Fighters in 2017.
Texas Rangers On December 15, 2017, Martin signed a two-year, $4 million contract with the
Texas Rangers. He recorded a 4.54 ERA in innings pitched in 2018. After the 2018 season, Martin represented MLB in the
2018 MLB Japan All-Star Series from November 8–15. When Rangers' closer
Shawn Kelley went on the
injured list in May 2019, Martin filled in for him. Martin and
José Leclerc received save opportunities when Kelley was injured in July. For the Rangers in 2019, Martin had a 3.08 ERA in 38 appearances; from May 24 to July 30, he had a 1.45 ERA. On September 11, Martin pitched an
immaculate inning in the bottom of the seventh against the Philadelphia Phillies. He had a 4.08 ERA with Atlanta in 20 games after the trade, finishing the season with a 3.40 ERA and four saves in 58 total appearances. The Braves included Martin on their roster for the
2019 National League Division Series, but he
injured an oblique muscle while warming up in Game 1 and was removed from the roster. A free agent after the 2019 season, Martin re-signed with Atlanta on a two-year contract worth $14 million on November 19. In the
pandemic-shortened 2020 season, he pitched to a 1.00 ERA in 19 relief appearances spanning 18 innings. In 2021, Martin had a 3.95 ERA in 46 relief appearances. Martin appeared in 34 games for the Cubs, recording a 4.31 ERA in innings. He recorded a 3.29 ERA in his appearances after June 17.
Los Angeles Dodgers On July 30, 2022, the Cubs traded Martin to the
Los Angeles Dodgers in exchange for
Zach McKinstry. He pitched innings over 26 games and finished 3–1 with a 1.46 ERA.
Boston Red Sox (second stint) On December 8, 2022, Martin signed a two-year contract with the
Boston Red Sox. He started the 2023 season as a member of Boston's bullpen, and spent two weeks during the second half of April on the injured list. Martin served as an effective reliever for the Red Sox, posting a 4–1 record with a 1.05 ERA in 55 appearances before being placed on the injured list on September 28 due to a viral infection.
Texas Rangers (second stint) On January 6, 2025, Martin signed a one-year, $5.5 million contract with the
Texas Rangers. In a 2–1 loss to the
Detroit Tigers on July 21, Martin suffered a left calf strain and was placed on the injured list. Martin returned from the injured list on September 1, earning the victory in relief during a 7-5 extra innings win over the
Arizona Diamondbacks. In 49 total appearances for Texas, he compiled a 2-6 record and 2.98 ERA with 43 strikeouts and two saves across innings pitched. On December 19, 2025, Martin re-signed with the Rangers on a one-year, $4 million contract. ==Pitching style==