Could I choose a PhD supervisor from a different university?
It is very unlikely, probably impossible, that you could have a primary supervisor from another university, especially in a different country.
You also really need someone at your doctoral university to guide you through the rules and such of that university. Someone from the States wouldn't be very good at that.
However, some universities permit co-supervisors, so that might be a possibility. It would be easier if your primary supervisor has a professional relationship, already, with the person you would like from the States. It would be up to the primary (local) supervisor to agree to such a relationship.
And bad things can happen if it turns out that your various supervisors don't agree on things.