Showing proficiency in a subject without taking a course
If showing proficiency in this one area is so essential to your application for graduate study that without it you would fail, then you are already in trouble. It would be different, of course, for a required undergraduate course such as Algorithms. If your general record is strong without this, then don't worry too much about showing proficiency for application to a program. You can mention in your CV or elsewhere that you have also studied machine learning on your own and it will be noted as a plus, even if unverified. 

The problem in general with evaluating self study is that it can vary so widely. It is hard to verify that you've studied in sufficient depth, but also that you have covered the ground that would be expected in an UG course. Of course, if you have written machine learning algorithms and tested them, then your code and results can speak for the depth, but not necessarily the breadth. 

However, if you want to study machine learning as a dissertation topic, then you need to convince one person, your advisor, that you have the necessary background. You can probably do that in an interview, which might have some aspects of an informal oral exam. 

In general, though, some advice to self studiers. Don't think that you have learned something just because you have read about it or were a relatively (or completely) passive participant in an online course. Solve a lot of problems, and save your working papers. Build yourself a portfolio, which can just be a stack of paper, that shows that you have engaged successfully with the subject. Attend to the breadth issue. If standard textbooks exist they can be a good guide to breadth and their exercises and suggested projects a good verification of depth, provided that you do them.