[4] The San Francisco Giants selected Stratton in the first round of the 2012 Major League Baseball draft.

[8] Stratton was called up from the Sacramento River Cats (AAA) to the majors on May 28, 2016, to replace the injured Matt Cain.

[9] Despite being primarily a starter in the minors, the Giants added Stratton to their bullpen and he made his major league debut against the Atlanta Braves on May 30, pitching a scoreless bottom of the eighth inning and recording two strikeouts while retiring all three batters he faced.

[10] On June 11, he was credited with his first major league win as he pitched the top of the 10th inning in the Giants victory against the Los Angeles Dodgers.

On September 14, 2018, Stratton threw his first MLB complete game against the Colorado Rockies, winning by a score of 2–0.

On August 1, 2022, the Pirates traded Stratton and José Quintana to the St. Louis Cardinals for Malcom Núñez and Johan Oviedo.

[21] On July 30, 2023, the Cardinals traded Stratton and Jordan Montgomery to the Texas Rangers in exchange for John King, Tekoah Roby, and Thomas Saggese.