Chance Of Getting A Research Internship In US/Canada For Non-US Residents?
You should simply send an email to the supervisor you are interested in. Your best help to be accepted to any program is to have the support of a professor. In US/Canada you should just start by, Dear Mr/Mme, X. 

Now, to convince the professor that you are a good fit, you need to convince him that you are have research potential. This is what the university will be looking for too.

You could talk to him about your interests, and how they recoup his (assuming they do by OP post). If you have done any research in that field you could mention it.

If you can find and read first a relevant paper he wrote and have questions about it, ask. I you can't because they are too complicated (which may really happen), or behind a paywall to which you don't have access, you could ask for a few classic references to get started.