AL West champion Texas also signed left-hander Donnie Veal to a minor league contract on Wednesday.
McKenry has appeared in the majors with Colorado (2010, 2014-15) and Pittsburgh (2012-13). He hit .215 with four homers and 17 RBIs in 59 games for the Rockies last season before surgery in August for torn meniscus in his right knee. He is a .239 career hitter in 308 games.
Veal had a 1.69 ERA in 17 games for Aguilas in the Dominican Winter League. He has made 105 major league relief appearances, going 3-3 with a 5.48 ERA for Pittsburgh (2009), the Chicago White Sox (2012-14) and Atlanta (2015).