Should I inform my potential advisor that my paper got rejected?

I don't think that being rejected by a top tier journal of your field should reduce your chances to get the PhD position in any way. Your potential advisor most likely knows this all too well. This is part of the scientific professional life. I would assume that s/he can judge the work you did regardless of his field of expertise our whether it got accepted or not. But if it was well written, presented in a clear and structured way, he or she will appreciate that because it is such an important skill.

You don't need to mention it yourself if you feel uncomfortable about that. However if you want, you can say that you got rejected by X, but think that with the feedback you got you can really improve the manuscript and will try to publish it elsewhere. This will show your motivation. Most likely your advisor will be happy about that.

I think this question really implies an underlying second question. Breaking it into two parts;

(1) Does getting a paper rejected look bad on your application?

(2) Do you have an obligation to tell your potential advisor?

In regards to (1), the answer is no, not really. Of course, if you had your paper accepted, that would be better...but only marginally. Papers get rejected all the time, even really good ones. One almost never gets a paper accepted on the first submission, so taking in the feedback from the reviewers and resubmitting is just a part of the process. Also, keep in mind the professor has already seen the paper. This means they know whether it's a good paper that got rejected as a part of the standard process, or whether it's just such a terrible paper that it will never be accepted. So I wouldn't worry at all about the potential advisor changing their opinion about you based on getting your paper rejected. The only way it would be very problematic is if you said something like "my paper got rejected and it hurt my ego so much I don't want to ever submit again" (PhD's require determination), or "my paper got rejected by a bunch of simpletons who clearly don't understand how great my work was" (arrogance is probably one of the harder traits to deal with in a grad student). On the other hand "my paper got rejected, but the reviewers pointed out a few ways I could clarify/improve my work so I'm going to fix it up and re-submit" is a great attitude to have.

In light of my response to (1), I think (2) is not such a big deal either way. I don't think you need to immediately email your potential advisor and tell him the news, that would be kinda weird. If he asks about the paper, you should certainly tell him. Whether you want to tell him if he doesn't ask is up to you. Personally, I think discussing that it got rejected and that you want to resubmit after cleaning it up shows a good attitude, so I would push for that. For example:

Maybe future advisor: "So what's new since last time we talked?"

You: "Well, just got back the decision on the paper we talked about. It got rejected, but the reviewers pointed out that I need to work on X and Y. So I'm going to clean it up and resubmit."

Nothing wrong with that. Nothing wrong with not discussing it if it doesn't come up in conversation either.

Side note: if the above conversation leads to an engaging discussion about the merits of X and Y with your potential advisor, that's just about the best interview you could have in regards to finding out how the advisor/student relation will work between the two of you.

You don't need to tell them as long as they don't ask. You did not lie in your application, that's all that count.