Here is a link from another forum that might help.
Is there such a thing as a carry-on garment bag?
I suggest calling the airline to see if you can bring a garment bag as carryon and if so, what dimensions. Failing that, I recommend packing the tux in your checked suitcase. My personal preference in packing business wear was to use a hard shell Samsonite) suitcase, which came with a rectangular removable frame with a clasp for a coat hanger (supplied). I hung the suit on the frame and folded it around the rectangle. This kept it flat. I always put a plastic dry cleaning bag over my suit and packed it in the middle of the suitcase. On arrival I would hang it immediately and in most cases it would hang perfectly by the next morning. If not, I ironed it, though steaming would be easier if you have access to a steamer.
Hope that helps. Mind you, I did once see someone bring a wedding dress aboard a flight (in a very long garment bag) which the flight attendant carefully hung in the coat rack in business class. A tux will be much easier!