Barton is renowned for his fiery temperament, and Warnock has first hand experience of managing the 33-year-old.
Warnock managed Barton during his time in charge at Queens Park Rangers, and he admits that the midfielder is not the easiest player to control.
However, the former Rotherham boss has backed Barton to be a success for Rangers - if he does curb his temper.
"I don't think even he knows if he will cope with it," Warnock said.
"But we saw a very mature Joey Barton last season. No-one expected him to go through a whole season without the red mist descending.
"If he can curb that red mist, it wouldn't surprise me to see him win the player of the season award.
"If Joey can curb that red mist, I think he will enjoy it in Scotland more than he has enjoyed his football for many years.”
Barton’s arrival at Rangers has created great excitement around Ibrox, as his signing shows Warburton’s side ambition.
Rangers are building a squad for their first season back in the Scottish Premiership.
Alongside Barton, Rangers have already added Matt Crooks, Jordan Rossiter and Josh Windass.
Warburton’s men are likely to make even further additions signings before the season starts, with the Glasgow club in talks with Steven Taylor today.