He'd have to already be naturalized, but yep! They did away with the age restriction on Mounties some time ago, before Ray's time even, so yeah. He definitely could! Admittedly, he wouldn't get any kind of special treatment for having been American law enforcement, I don't believe, but if he wanted to do it, he could.

I have heard of naturalized Canadians applying, though none specifically who were prior US LEOs. But it's not unheard of; here in the US, we actually had a British citizen working for a local department, though the laws here only require that they've got a permanent residency visa. Up there, you have to have full citizenship.