Miller is hitting .205/.350/.318 with just two homers this season, but leads the American League with 30 walks.
Martinez, 34, is a seven-year veteran with Major League experience at six different positions. He was designated for assignment by Cleveland on May 14. Martinez hit .257/.289/.331 over parts of three seasons with the Indians, and appeared for them in the World Series last fall.
To make room for Martinez on the 40-man roster, the club transferred left-hander Xavier Dedeno to the 60-day disabled list.
Joe Trezza is a reporter for MLB.com based in New York. Follow him on Twitter at @joetrezz. This story was not subject to the approval of Major League Baseball or its clubs.