The AL champions on Friday also purchased the contracts of right-handers Fabio Castillo and Wilmer Font, left-hander Miguel De Los Santos and outfielder Engel Beltre, adding them to their 40-man roster.
Cash appeared in 49 games for Houston and Boston last season. He has played 246 major league games with Toronto, Tampa Bay, Boston, the New York Yankees and Houston.
Deeds spent all of last season at Triple-A Reno in the Arizona organization, batting .302 with 12 homers, 39 doubles and 55 RBI.
Texas outrighted German earlier this month.