Rodriguez hurled 1.2 scoreless frames in a relief appearance against Toronto on Friday. He allowed no hits and two walks while striking out a pair.
Rodriguez struck out three while allowing two hits and one walk in two innings Friday against the White Sox.
Rodriguez has made the Angels' Opening Day roster, Mike DiGiovanna of the Los Angeles Times reports.
Angels manager Joe Maddon suggested Sunday that Rodriguez profiles as a reliever both now and in the future, Jeff Fletcher of The Orange County Register reports. "If you look at (Rodriguez) right now, he looks like a relief pitcher to me," Maddon said. "But that doesn't mean he can't start. Just looking at the way he comes after you, the physical stuff, how intimidating he can be in the short term, it's very interesting. I've not seen enough of him to know the other side of it."
Rodriguez is being considered for an Opening Day bullpen spot, Fabian Ardaya of The Athletic reports.
Rodriguez struck out both batters he faced Tuesday versus Cincinnati.
Rodriguez was added to the Angels' 40-man roster Friday.
Rodriguez will be part of the Angels' 60-man roster.
Rodriguez (back) has recovered from back surgery and threw a bullpen session in early March, Rhett Bollinger of MLB.com reports.
Rodriguez underwent surgery for a pars defect (a stress fracture in his lower spine) Friday, Fabian Ardaya of The Athletic reports.