The 34-year-old recorded a 5.04 ERA over 45 triple-A appearances in 2019.
He last pitched in the majors in 2018, splitting his time with the Seattle Mariners and Cleveland Indians.
Rzepczynski was a fifth-round pick by the Blue Jays in 2007, spending his first three seasons in Toronto.
Over the course of his 10-year career, Rzepczynski has compiled a 14-27 record with a 3.89 ERA and a 1.436 WHIP with stints also in St. Louis, Oakland, San Diego and Washington.
Montoyo also revealed that left-hander Ryan Borucki is “behind” after being shut down early in spring training with elbow tightness.
The 25-year-old struggled with elbow problems all of last season, making just two starts in the majors before having surgery to remove bone spurs in August.