If the wood has separated into two pieces it is better to drill it and put either a small piece of threaded bar in or a hardwood dowel.

You can line the two halves up by knocking a panel pin part way in and then snipping the head off. Press the half with the panel pin into the other half and it will mark the wood ready for drilling so it lines up. Take the panel pin out and drill that half as well.
Don't forget if you are using any glue you will need a small air hole drilling to let the trapped or out or what you put in will be like a piston and the trapped air will keep pushing you bar or dowel out.