Parker was selected in the 28th round of the 2018 Major League Baseball draft by the Chicago Cubs, but opted not to sign with the team.

[2] Parker was selected in the 27th round of the 2019 Major League Baseball draft by the Tampa Bay Rays, but decided to return to San Jacinto for a second season.

[3] The Washington Nationals selected Parker in the fifth round of the 2020 Major League Baseball draft.

[6] He was promoted to the High-A Wilmington Blue Rocks on July 13, 2021, after going 3–7 with a 4.08 ERA and 85 strikeouts over 57+1⁄3 innings pitched with Fredericksburg.

[9] On April 15, 2024, the Nationals promoted Parker to the major leagues for the first time, optioning Amos Willingham to Triple-A to making room for the former on the active roster.