There's no immediate way he can come to Canada.
Since he's applied for refugee status in the US, any sort of temporary status application to Canada (visitor visa, study permit, work permit) will be refused. Nothing will change if you get married.
The only realistic option I see for having him come to Canada is for the two of you to get married and for you to apply for PR once you qualify and include him in the application. Once the PR application is approved, he will be able to come to Canada. But since you're in Canada on a study permit, it's likely going to be years before this is possible.