Well... Morning glories are vines. Then again, so are Wisteria and those can be trained into tree-form. If you cut the plant back it will make your plant bushier (because the apical bud contains a hormone suppressing lateral growth). Don't cut it back by more than 1/3 though. I think MG are tropical so I don't know how much floral success you'll have, although I hope you have a lot!
OoOoOrrrrr you could put it outside and let it grow all over your railing. Now wouldn't that be nice, and save the inside spot for a more-suited-for-indoor plant?? If you bring it outside make sure to temper it, that is, bring it out for a few hours later in the day when it isn't so hot, bring it back in, put it out again the next day, bring it back in, put it out for longer the next day, etc, until it can be released from captivity (lol).
"Don't you know we are the roots that hold this tree, feeding the branches and all of its leaves?"