The Czech Republic international scored both the Gunners' goals in their 2-1 win at The Hawthorns to keep the pressure on rivals Chelsea and Tottenham Hotspur in the race for the Champions League spots.
Rosicky, who has found himself largely out of the team this season, hopes that his current purple patch can cement his place in the starting lineup.
"It's difficult when you're not playing," Rosicky told ESPN. "You want to be part of the team.
"[The] only way you can get into the team is through hard work. You have to convince the manager that you're part of the team. That's what I am trying to do. Everyone wants to play.
"I am very glad to contribute again. I hope I can continue like that."
The match marked the 32-year-old's second start of the campaign.