Rigney was one of the Chicago White Sox top pitchers in the years prior to World War II.

Following his playing retirement, Rigney took a position in the White Sox front office, becoming farm system director in 1947.

In October 1955, he became the club's co-general manager, along with brother-in-law Chuck Comiskey, replacing Frank Lane.

He departed the post when his wife sold her 54 percent share of the White Sox to Bill Veeck in 1959.

In an eight-season career, Rigney posted a 63–64 record with 605 strikeouts and a 3.59 ERA in 197 appearances, including 132 starts, 66 complete games, 10 shutouts, five saves, and 1,186+1⁄3 innings of work.