At one time I would have said yes, but I hear my daughter saying, "Can I get...?" and she is not at all a rude person. I think it is just another way of asking. Language does change and, as another commentator has put, it depends on where you are in the world; I am told that US citizens view the 'have' as strange, whereas, to us old Brits, "Can I get....?" suggests the answer - "Well, yes, you can, but I won't be giving it you!"
I really would prefer a, "please" tacked on to the front.