The outspoken former England international knocked back the chance of another crack at the Barclays Premier League with Burnley in order to sign for Mark Warburton's Light Blues.
He reckons he is about to show Hoops midfielder Brown - who is looking to lead his side to their sixth straight title - who is boss.
Barton has already claimed his aim next season is to make himself the best player in Scotland and he went further while guesting on TalkSPORT's breakfast show with Alan Brazil.
Asked if he will be a marked man in Scotland, the 33-year-old said: "Of course, that's the nature of being me. It comes with the territory.
"But without being disrespectful to the players up there, people keep talking about Joey Barton v Scott Brown. He's not even in my league - he's nowhere near the level of player I am.
"He can't get near me. If I play well, Brown does not stand a chance. That's not me being blasé - that's just me stating what I believe."
The former Manchester City, Newcastle, QPR and Marseille battler was a pivotal figure for Sean Dyche's Clarets last term as they won a ticket to England's top flight by topping the SkyBet Championship.
He insists he is not ready to slow down yet, even if Scotland's top flight cannot boast the riches on offer down south.
He said: "If people are going to have a different opinion ... it's not going to be Joey Barton v Scott Brown. It's Glasgow Rangers v the rest of Scottish football. There's some good sides, some really good players. It will be competitive.
"I'm expecting I'll have to be at the best of my ability for Rangers to do well. But I'm trained and ready to go. I'm not going up there thinking I can just turn up.
"I've played against Scottish players south of the border and they all give you a game. Everyone's at it. I've been a marked man for 10 years and a lot of that is my own doing.
"But you know what? I'm comfortable with that. I'm comfortable with expectation, with pressure, with my own focus and performance.
"If I get to that level then unfortunately for everyone up there, they won't be able to live with me."