Rossiter was on the books of Liverpool from 2003 until the end of the 2015-16 season.
The 19-year-old midfielder joined Rangers in the summer transfer window and has arrived at Ibrox with a strong reputation.
The England Under-19 international is a very promising young player, and he is determined to do well at the Gers.
Rossiter has revealed the advice he was given by Carragher when he was at Liverpool.
Carragher is one of the greatest defenders in Liverpool history and was at the Reds for his entire career.
“At Liverpool it was a good group of lads and there are a lot of players,” Rossiter told The Glasgow Evening Times.
“When I was coming through, the likes of Jamie Carragher and Steven Gerrard are the Scouse lads that you look up to and have been at the top level.
"So you always look towards them. They put their arm around you and when they see you out on the pitch they help you out.
“I remember Jamie was saying to always be yourself and don’t be scared to show your personality. Get on the ball and get your tackles in. That is what I want to do.”
Rangers won the Scottish Championship title last season and will feature in the Scottish Premiership during the 2016-17 campaign.
Mark Warburton’s side will be expected by many to compete with Old Firm rivals Celtic for the Scottish Premiership title this season.
The Gers have been quite busy in the summer transfer window so far, signing Joey Barton, Clint Hill, Niko Kranjcar and Lee Hodson among others.