Cory Abbott competed at Cooperstown Dreams Park during Week 1 in 2006 with the San Diego Stars South (CA).

A right-handed pitcher, Cory graduated from and played baseball at Junipero Serra High School (San Diego, CA) where he went 7–2 with a 1.52 ERA his senior year. Cory continued his education and baseball career at Loyola Marymount University (Los Angeles, CA). Prior to his junior year (summer of 2016), Cory played collegiate summer baseball with the Orleans Firebirds of the Cape Cod Baseball League. During his junior collegiate season (2017), Cory went 11-2 with a 1.74 ERA and threw the first perfect game in school history.

Cory was drafted by the Chicago Cubs in the 2017 Major League Baseball draft. At the conclusion of the 2019 season, he was named Cubs Minor League Pitcher of the Year.

He made his major league debut on June 5, 2021. He was traded to the San Francisco Giants in April 2022 and then the Washington Nationals in May 2022.