Baseball America rated Peacock the 42nd best prospect in baseball during the 2011 season.[3] He represented the Nationals at the 2011 All-Star Futures Game.[4] He was named a starting pitcher on Baseball America's 2011 Minor League All Star team.[5]
Peacock began the 2011 season with Harrisburg and also played for the Syracuse Chiefs of the Triple–AInternational League. He was promoted to the majors and made his MLB debut on September 6, 2011.[1] He earned his first major league win on September 14.[6]
Peacock began the 2013 season at the Triple–A level before being called up by the Astros. He pitched to a 5.18 ERA in 83+1⁄3 innings. In 2014, he pitched a career-high 24 starts (28 games total), finishing 4–9 in 131+2⁄3 innings.
Peacock was out of options in 2017, and so could not be sent to the minor leagues.[9] He began the season as a relief pitcher, with a 1.10 ERA in 16+1⁄3 innings pitched, and received a spot start on May 22 in place of the injured Dallas Keuchel.[10] Following a start in which Peacock allowed one hit and no runs in 4+1⁄3 innings, Peacock replaced Mike Fiers in the starting rotation.[11]
In 2018, Peacock pitched the whole season out of the bullpen, totaling 61 appearances. He struck out 96 batters in 65 innings. He was 3–5 with three saves and had a 3.46 ERA.
On May 8, 2019, Peacock threw a career-high 12 strikeouts in 7 innings against the Kansas City Royals. In 2019 he was 7–6 with a 4.12 ERA, and struck out 96 batters in 91+2⁄3 innings. Peacock only appeared in 3 games for the Astros in 2020, registering a 7.71 ERA with 3 strikeouts in 2+1⁄3 innings of work.[14] He became a free agent after the season.
Cleveland Indians
On June 25, 2021, the Cleveland Indians signed Peacock to a minor-league contract.[15] He was assigned to the Columbus Clippers of the Triple-A East. Peacock made 11 appearances for Columbus, going 0–4 with a 7.68 ERA and 38 strikeouts in 34 innings.[16]
Boston Red Sox
On August 30, 2021, Peacock was traded to the Boston Red Sox in exchange for cash considerations.[17] The following day, the Red Sox selected Peacock's contract;[18] he started that evening's game against the Tampa Bay Rays,[19] taking the loss after allowing five runs on two hits in 2+1⁄3 innings.[20] He was subsequently returned to the Triple-A Worcester Red Sox and removed from the 40-man roster.[21] He made two relief appearances with Worcester; in two innings pitched, he allowed three runs while striking out three batters.[16] On November 7, Peacock elected free agency.[22]
Kansas City Royals
On March 8, 2022, Peacock signed a minor league contract with the Kansas City Royals.[23] On July 18, he was released by the Royals.
Minnesota Twins
On July 29, 2022, Peacock signed a minor league contract with the Minnesota Twins. In 20 appearances for the Triple-A St. Paul Saints, he posted a 3-3 record and 3.38 ERA with 22 strikeouts and 8 saves across 21+1⁄3 innings pitched. Peacock elected free agency following the season on November 10.[24]
Peacock's father, Jerry, converted a trailer into a camper in order to follow Brad in the minor leagues.[26] Peacock and his wife, Stephanie, had a son in June 2017.[27]