The 33-year-old winger has been training with the English League Two side in recent weeks as he looks to get his career back on track following his release from Preston North End over the summer.
Sinclair enjoyed the most successful period of his career during a three-and-a-half year spell under Brendan Rodgers at Parkhead between 2016 and 2019.
Now the former England Under-21 international has return to the club where he made his professional debut at the age of 15 in Decemebr 2004, and is in contention to face table-toppers Plymouth Argyle for the first time in 18 years after he left to join Chelsea as a teenager.
Sinclair spent five years at Stamford Bridge where he was loaned out to various clubs before joining Swansea City. From there, he earned an £8million move to Manchester City but after failing to make an impact, signed for Aston Villa.
It wasn’t until he headed north of the border to Glasgow’s West End did Sinclair’s career begin to flourish, playing a vital role as part of the Invincible Treble-winning team in the first season.
He left the Hoops in May 2019 after lifting three Premiership titles, three Scottish Cup and three League Cups in his time at the club.
Speaking to Rovers official website, Sinclair said: “I’m delighted to back at the place where my career began. I’ve been training for a couple of weeks and The Quarters is certainly very different to where we trained when I was younger!
“I’ve always wanted to come back to the club to give back what they’ve given me at the start of my footballing journey.”
Rovers boss Joey Barton commented: “We are delighted to have brought Scott into the group. He has been training with us for a couple of weeks now. We’re enjoying having him in with us. He’s a fit lad, his experience and quality is superb and he will strengthen us further as we move into these winter months.”