Calvin, this has happened to me a few times, but it’s pretty easy to fix. I once had to do it in a hotel with material I bought at the dollar store. You’ll need wood glue (don’t use superglue or that sort of thing, as you won’t be able to take it apart if you make a mistake), sandpaper, and a clamp or vise or something like that.
Clean off any glue that is still on the surfaces you will be re-gluing, this might be best done with fine sandpaper - just be sure not to take off any wood. Wipe the area with a damp cloth, let it dry, then apply the glue, align the two pieces and clamp it together. I let mine dry overnight, and that seemed to be fine. Be sure when you align the pieces that they fit together as tightly as possible. Getting this right is important because it will effect the angle of the neck in the shamisen. If you get it wrong, and use wood glue, you can always re-glue it, but if you’re careful the first time it should be fine.