"Thought he threw the ball very well this spring," D-backs GM Kevin Towers said.
The team plans on using Rowland-Smith in long relief, along with right-hander Josh Collmenter.
Having another pitcher who can throw multiple innings in the bullpen became a priority given starter Bronson Arroyo's struggles with a bulging disc this spring and the season-ending injury to ace Patrick Corbin.
The decision to carry 13 pitchers meant that shortstop Didi Gregorius could not make the team in a bench role.
The team is likely to go back to 12 pitchers when outfielder Cody Ross returns from his hip injury, which could be a week to 10 days after the season begins.