After signing, Peterson made his professional debut that year with the Brooklyn Cyclones and spent the whole season there, going 1-1 with a 6.26 ERA in 23 innings pitched in relief. In 2013, he pitched 17.2 scoreless innings for Brooklyn, and in 18 games pitched for the Savannah Sand Gnats, he was 1-0 with a 5.13 ERA. Peterson began 2014 with Savannah, and after pitching to a 3-0 record and 2.05 ERA in 19 relief appearances, he was promoted to the St. Lucie Mets where he was 2-1 with a 5.70 ERA in 23.2 relief innings pitched. He also pitched in one game for the Binghamton Mets at the end of the season. Prior to the 2015 season, Peterson received an 80-game suspension after testing positive for a performance-enhancing drug.[2] After serving his suspension, he played for Savannah where he compiled a 1-0 record and 1.69 ERA in 16 relief appearances. In 2016, he pitched for both St. Lucie and Binghamton, pitching to a 4-1 record and 3.03 ERA in 62.1 innings pitched out of the bullpen. In 2017, he pitched two games for the Las Vegas 51s along with 41 games for Binghamton in which he was 5-3 with a 1.14 ERA.[3] He began 2018 with Las Vegas.
Peterson was called up to the majors for the first time on May 30, 2018.[4] He made his debut that night against the Atlanta Braves at SunTrust Park, allowing a home run to Johan Camargo in two innings of work.[5]
Peterson was called up to the majors on May 5, 2019 after starting the season with the Syracuse Mets.[6] He appeared in one game and was sent down the next day on May 6.[7] On August 16, 2019, Peterson was designated for assignment. He elected free agency on October 1.
On July 13, 2022, Peterson's contract was purchased by the Leones de Yucatán of the Mexican League.[10] In 10 games for the team, Peterson worked to a 4.66 ERA with 12 strikeouts and 7 saves in 9+2⁄3 innings of work. Peterson won the Mexican League Championship with the Leones in 2022.[11]
In 2023, Peterson pitched to a 0–1 record with a 3.24 ERA and 11 strikeouts over 16+2⁄3 innings of relief.
Algodoneros de Unión Laguna
On July 3, 2023, Peterson's rights were traded to the Algodoneros de Unión Laguna of the Mexican League.[12] In 7 relief outings, he posted a 4.70 ERA with 5 strikeouts across 7+2⁄3 innings pitched. On February 26, 2024, Peterson was released by Unión Laguna.[13]