Is it a smart idea to ask my manager what rank in the team I got for
this performance review?
Unless your company is in the habit of ranking each individual within the team, it's not a smart idea. (You could ask your manager if your company requires ranking.)
Generally, individual performance reviews are confidential. And generally managers don't want to get into a discussion about if you should have been ranked #9 instead of #12. Unless you are told you are #1 or #30, you won't know who is ahead of you or who is behind you.
And rank is not relevant (again unless the company is in the habit of ranking for pay raise purposes).
You would be far better served to concentrate on your performance and your own reviews rather than the reviews of anyone else. You career/pay/progress is impacted by what you do. If you are terrific, it doesn't matter if everyone else is terrific too. And if your performance is poor, it doesn't matter if others' performance is poor too.
Ask for your manager's perception of you if that's what you seek. Don't try to back into a calculation of it based on an irrelevant ranking.
Ask what "meets expectations" really means. Ask what "above expectations" means. And most of all, ask what you can do to get better performance reviews. Ask for specifics, based on what was written in your review, and what work you have in front of you for the upcoming year.
Focus on you, and what you can control.