A native of Worcester, Massachusetts, Ryan attended the College of the Holy Cross. He posted a 9–2 win–loss record as a pitcher in his freshman year, and threw the school's first no-hitter, a 4–0 victory over Dartmouth at Fitton Field in 1918. Ryan graduated from Holy Cross in 1920.
Ryan went 15–8 with a 1.36 earned run average (ERA) for the Buffalo Bisons of the International League in 1919, and was called up by the New York Giants late in that season. He made his major league debut on September 7, getting the start on the mound in the second game of a doubleheader against the Boston Braves at the Polo Grounds. The game featured a pair of Baseball Hall of Famers at shortstop in Boston's Rabbit Maranville and the Giants' Frankie Frisch. Ryan twirled five innings, allowing eight hits and three earned runs, taking the loss in the Giants' 4–2 defeat. Ryan appeared in four games for the Giants that season, then had another impressive season in the International League in 1920 with the Toronto Maple Leafs, and appeared in three games for the 1920 Giants.
Ryan became a Giants regular in 1921, appearing in 36 games, and posting a 7–10 record with a 3.73 ERA in 147.1 innings. He had an impressive three-week stretch from July 4–24, tossing four complete game wins, including a 10-inning 4–3 win against the St. Louis Cardinals and Hall of Famer Rogers Hornsby, who accounted for three of the Cards' six hits off Ryan. Despite his solid regular season performance, Ryan did not appear in the postseason as the Giants went on to claim the 1921 World Series over the New York Yankees and slugger Babe Ruth.

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