Byrd, 30, signed with Texas as a free agent on Dec. 8, 2006. He began 2007 with Triple-A Oklahoma, and hit .358 with six home runs and 32 RBI in 44 games before being recalled on May 26.
Byrd spent the remainder of the season with the Rangers, batting .307 with 10 home runs and 70 RBI in 109 games and 414 at-bats. He posted a .356 average at Rangers Ballpark.
Catcher Gerald Laird is the only Rangers player who is eligible for arbitration.