The Gunners going into the weekend top of the table after victory over Bolton Wanderers.
"We are definitely up for the title," Rosicky told arsenal.com.
"I think everybody knows that the coming weeks are the critical ones in the whole season and I would say the win over Bolton came right on time for the team. For the confidence of the team, it is absolutely great.
"I think the togetherness in this side is very good. If you don't have this, you don't turn games around. It is very important that this characteristic is in the team."
The Czech midfielder believes consistency will be the key to winning the Premier League and hopes Arsenal can continue their unbeaten run of form.
"Since the loss against Chelsea we started something new again and went on a run," he said. "You can see how quickly it can change in this league.
"Chelsea didn't win a few games after winning here. You have to be consistent and that's what we want to be."