Can I use this idiom when I talk about “studying”?
I’m going to Canada to study and learn the ropes of English.
It doesn’t seem right to me, but I don't know.
As a native speaker, I agree with Colin Fine and wouldn't use this.
Learn the ropes is defined as:
If you learn the ropes, you learn how to do a particular job or task.
It isn't really used in relation to a new language/subject.
I would say:
I’m going to Canada to study and start my learning experience in English,
learning experience indicates you are new to English and fits well in your sentence.