My potential future PhD supervisor ask me to peer review a paper
Maybe it's a matter of question formulation, but I find this to be a very peculiar request and would be equally confused as you seem to be even if I wasn't busy with other stuff. 

Specifically, you're not qualified to review a paper, yet.

If he's asking your analytical opinion on a paper, kind of like a journal club style dissection of the content, then sure I guess that's no big deal. But if you are given a manuscript, written by someone else and submitted to a journal, I find this request unrealistic and even unethical. 

Also, in a way disagreeing with the previous answers here, I don't think it's a reasonable request even if you were given the article in a more relaxed, journal club-like format. Because you are supposed to learn to read and understand the scientific literature, it's part of your training as a PhD student. To use that during the recruitment process, as a test is a bit unfair in my eyes. 


  that was my first feeling actually, that he was assigning me some of
  his work while I am still in the application phase. The paper is
  anonymous and I am asked to peer review it for a journal publication.


The above alone, would even deter me from considering to start there. I think it might be worth thinking about what kind of work environment you want to get yourself into for the coming 3-X years of your life.

But again, it's possible that I misunderstand something in the OP. Just my two cents...