The Rangers announced the move after their 4-3 loss in 12 innings at Cleveland on Sunday.
Texas also transferred right-handed pitcher Alexi Ogando from the 15-day disabled list to the 60-day DL.
The 28-year-old Carp batted .198 with no homers and nine RBIs in 42 games for Boston this season. The lefty hitter was designated for assignment by the Red Sox on Friday.
Carp missed more than a month in the middle of the season because of a broken right foot.
Carp is a career .260 hitter with 27 home runs and 123 RBIs in parts of six seasons with Seattle and Boston.