Yes you can use a high quality wood glue such as
Titebond II but I would recommend a super strength wood epoxy such as
PC Woody or
Loctite for wood repair.
You will need to clamp any of the parts if at all posible and I recommend using wax paper between the clamp and wood for protection.
The Titebond will take 24 hours to set up completely.
The PC Woody will need about 3-4 hours to set up and the Loctite will set up in less time than that.
Just a note: I've been using the Loctite with great results but I need to warn you the intial hardening of the product takes place in under 4 minutes so work fast!
