The White Sox released Walsh on Tuesday.
Walsh signed a minor-league contract with the White Sox on Tuesday, LaMond Pope of the Chicago Tribune reports.
The Rangers designated Walsh for assignment Saturday.
Walsh is not in the starting lineup for Friday's game against Atlanta.
Walsh is out of the lineup for Thursday's game against the Tigers.
Walsh is not in the lineup for Wednesday's game in Detroit.
Walsh is out of the lineup for Sunday's game at Houston.
Walsh is out of the lineup for Thursday's game against the Athletics.
Walsh is out of the lineup for Tuesday's game against Oakland.
Walsh went 2-for-4 with a run scored in Tuesday's 5-2 loss to the Rays.