Grossman started in left field and went 1-for-4 in Sunday's 3-1 loss to the Rockies.
The Rangers acquired Grossman from the White Sox on Wednesday in exchange for Anthony Hoopii-Tuionetoa.
Grossman went 2-for-3 with a double and a stolen base in Sunday's 5-1 win over the Cardinals.
Grossman is out of the lineup for Wednesday's game against the Twins.
Grossman is not in the lineup for Tuesday's game at Minnesota.
Grossman is starting in right field and batting second in Sunday's game against the Phillies.
Grossman isn't in the White Sox's lineup for Saturday's game against the Phillies.
Grossman is out of the lineup for the first game of Wednesday's doubleheader with the Royals.
Grossman went 1-for-3 with two walks, two runs and a stolen base Wednesday against the Guardians.
Grossman will get an extended chance to serve as the White Sox's leadoff hitter, Daryl Van Schouwen of the Chicago Sun-Times reports.