Translation:A drink, please.
Agreed. It looks like "Can I get something to drink?" and "Can I get a drink?" might be the only accepted translations right now. I tried everything I could think of, including "May I have a drink?", "Can I have a drink?", and even "A drink, please". I gave up after a while and typed "Can I get a drink" just to pass the question.
I've heard both ways in Engeland, my friend from the U.S. usually goes with "have" and "please" in these situations.
I am no native in English (rather bilingual) but I'm inclined to be very sceptical of this whole "American vs English" thing, the more I see it the less I think anything of that is actually true.
But yes, "can I have ... please" would fit a studying setting more, I think.
I wrote "a drink, please", and got "Can i've (sic) a drink, please?" like. Nope! Reported.