I agree with Phil that "plastic cup" would be the preferred translation. However, I have heard people ask for a 'plastic glass' without getting weird looks. In fact, many stores advertise "plastic wine glasses" -- see http://www.amazon.com/Chinet-Stemless-Plastic-Glasses-Count/dp/B00R0GIY0A/

It depends exactly what kind of container it is, but most likely you mean to say "a plastic cup." By the way, you are correct to imagine that if you say a "plastic glass" people may think you're weird…. Btw, have you heard English speakers use the term "boiled ice?"