The 22-year-old joined the Gers from Liverpool in 2016 but has failed to live up to expectations at the club.
In the past three seasons, he has only managed 16 appearances in all competitions, with recurrent injuries hampering his growth.
The former Liverpool midfielder spent the second half of last season with Ryan Lowe’s Bury, where he played a big role in helping them win promotion from League Two.
Rossiter made five appearances under Steven Gerrard last season, scoring once. He becoming Barton’s fifth summer signing is subject to international clearance.
Rangers boss Steven Gerrard has a wealth of midfield options, and Rossiter would have struggled to get regular games at the club.
The Gers further bolstered their midfield area by signing Joe Aribo this summer, and therefore sending him away on loan makes a lot of sense.
Some Rangers fans took to social networking site Twitter to express their reactions. Here are some of the selected tweets:
Dont care what anyone says he is a good player whoncould easily do a job for us if stays fit….
— 🔴⚪️🔵andybell🔴⚪️🔵 (@andyb29) July 8, 2019
Just a pitty about his injuries cause he is a cracking player
— It’s coming home (@bluekid877) July 8, 2019
Good luck to the lad as he obviously has talent. Why do we loan players to such lower leagues though? I would loan him to an SPL club for a season.
— AlternGr8 (@somethingfunks) July 8, 2019
One day this lad will be a starter for us…one day…one day 😭
— Merk (@rfcmark26) July 8, 2019
Should’ve just sold him
— Kevin Wakeham (@KWRFC1995) July 8, 2019
Hopefully he does brilliant like Bury and earn himself a new deal with us. If he stays fit I think he could be excellent. Absolutely loved what I seen when fit.
— Andy Rorison (@joshjnr1975) July 8, 2019
Another good season and he could be a starter for us . Certain of it.
— Gordon Smith (@Gord07) July 8, 2019