In the 2013 Major League Baseball draft, Girodo was selected in the 9th round by the Toronto Blue Jays, and assigned to the Class-A Lansing Lugnuts. In 14 appearances that season, he would post a 1–1 record, 4.18 ERA, and 24 strikeouts in 23 innings. In 2014, Girodo was assigned to the Advanced-A Dunedin Blue Jays for the entire season. In 47 appearances totalling a career-high 76 innings, he pitched to a 7–3 record, 2.47 ERA, and 81 strikeouts. Girodo began the 2015 season in Dunedin, where he was a Florida State League mid-season All-Star. He was promoted to the Double-ANew Hampshire Fisher Cats in June, and to the Triple-ABuffalo Bisonsin September. In 45 total appearances in 2015, Girodo would post a stellar 1.34 ERA, 4–2 record, and 58 strikeouts in 60 innings. During the offseason, he appeared in 7 games for the Salt River Rafters of the Arizona Fall League, recording a 1.80 ERA in 10 innings pitched. Girodo was invited to Major League spring training on January 12, 2016. He was assigned to minor league camp on March 25. Girodo was assigned to the Buffalo Bisons to open the 2016 minor league season. He made 4 appearances for the team, posting a 2–0 record, 1.35 ERA, and 7 strikeouts in 6 innings prior to his call-up.
Toronto Blue Jays
On April 22, 2016, Girodo was called up by the Blue Jays. He pitched two scoreless innings in relief that evening against the Oakland Athletics in his Major League debut. After Brett Cecil was placed on the disabled list, Girodo became the main lefty specialist for the Blue Jays. He was optioned back to Buffalo on April 23, and recalled on May 3. Girodo was optioned back to Buffalo at the end of May, and recalled by the Blue Jays on June 15. On February 9, 2017, Girodo was designated for assignment by the Blue Jays. After clearing waivers, he was assigned to Triple-A Buffalo and invited to Major League spring training. Girodo spent the entire season in the minors, going 2–4 with a 2.96 ERA in 31 games. On January 24, 2018, the Blue Jays invited Girodo to spring training. He was released on April 25.
Girodo was signed to a minor league contract with the Los Angeles Dodgers on May 7, 2018, and was assigned to the AA Tulsa Drillers. He pitched in seven games for the Drillers and six for the Oklahoma City Dodgers before he was released on June 16.