So, I figured this out a few weeks or so ago:
Take about a quart of Great Value orange juice (I used the calcium fortified kind, but I imagine the regular kind is at least as good). Add about a half a teaspoon of baking soda (give or take some; experiment to see if less works). Stir for about 45 seconds. It should be carbonated by now. Drink!
You may notice that the baking soda doesn't make it taste worse. It actually makes it taste creamier, instead of bitter (unless you added too much baking soda). Oranges are already kind of bitter (so that's probably why).
Anyway, it's delicious.