Ramsey has made two late substitute appearances for the Scottish champions so far, in their Premiership wins over Hearts and Hibs at Ibrox, since his deadline-day loan move from Juventus.
The 31-year-old has not started a club fixture since the opening day of the Serie A season last August, while his last start in any competition was for Wales against Belarus in a World Cup qualifier in November.
As he builds up his fitness levels, Ramsey has now convinced van Bronckhorst his involvement can be stepped up.
“Yes, he will start (against Annan),” said the Dutch coach. “Aaron has been doing well. He had more team sessions in training and some more minutes against Hibs on Wednesday. He is getting better and fresher and the rhythm is coming back, so he will be starting.”
As Rangers look to book their place in the quarter-finals of the Scottish Cup, the trip to League 2 promotion contenders Annan will also see Swedish international defender Filip Helander make his comeback after being sidelined for five months by the knee injury he suffered in a Premiership fixture against St Johnstone at McDiarmid Park.
"Filip is already training for some weeks now,” said van Bronckhorst. “I think he has had around 20 sessions with the team now, so we have him on a level where he can start games. He will start at Annan, so I am really happy for Filip that he can leave his injuries and the time he was off behind him.”
Van Bronckhorst was also pleased to report encouraging injury updates on defender Leon Balogun, who limped out of the midweek game against Hibs, and midfielder Ryan Jack who suffered an ankle knock in a challenge from Hearts’ Beni Baningime at Ibrox last Sunday.
"Leon had a scan which was very positive so the injury isn’t bad,” said van Bronckhorst. “Hopefully, he can return soon to join the team in training. Ryan, I think, will be available for training this weekend. For him, his ankle is recovering well and he should be involved in the game (against Borussia Dortmund) next week.”