Giovanni van Bronckhorst’s men received automatic passage through to the last 16, bypassing the group stages along with Celtic, Hearts, Dundee United and Motherwell, due to their involvement in European competition.
A number of changes are expected for the home side as van Bronckhorst looks to rest some of his key first-team stars amid a busy schedule and ahead of the first Old Firm showdown of the season at Celtic Park on Saturday.
Queens came through the group stages after finishing ahead of St Johnstone to qualify as one of the best placed runners-up behind Group F winners Annan Athletic.
However, the Doonhamers have made a disappointing start in the league, winning only one of their opening five fixtures to sit near the bottom of League One following their relegation from the Championship last season.
Here is all you need to know ahead of the fixture …
Who: Rangers v Queen of the South
What: Premier Sports Cup last 16
Where: Ibrox Stadium, Glasgow
When: Tuesday, August 30, 7.45pm kick-off
Is Rangers v Queen of the South on TV?
The cup clash will be broadcast live on Premier Sports. Coverage begins at 7.15pm on Premier Sports 1.
The match can be live streamed by subscribers on the Premier Player.
BBC Sportsound will have radio coverage of the match.
Rangers could make up to 10 changes with young striker Robbie Ure in line to make his first-team debut with Antonio Colak rested after netting seven goals in his last seven games. Fellow youngster Adam Devine is also lined up for a start in place of captain James Tavernier at right-back. Veteran goalkeeper Allan McGregor could also make his first appearance of the season after losing his number one status to John McLaughlin.