Rodriguez (lat) tossed a live batting practice session Sunday and could be activated for Tuesday's series opener against Oakland, T.R. Sullivan of MLB.com reports.
Rodriguez is traveling with the Rangers on the current road trip and could join the team immediately. The left-hander could be added to the committee of relievers that will pick up save chances with closer Jose Leclerc (shoulder) on the 45-day injured list. Before dropping him into high-leverage spots, the Rangers would probably want to give him a few soft appearances.