I like either Cyanoacrylate (also known as CA or Superglue) or a urethane glue. For a very narrow crack like that where you can't spread it apart much without the danger of further cracking I'd go with CA glue. In general I like urethane glue (like Gorilla Glue) better but it is thicker and I think you are going to want to get a hypodermic needle to inject that glue into the crack. Most urethane glues are just too viscous to push through a fairly fine needle.
Speaking of hypodermic needles, you can generally get those at feed stores, especially if they have a tack shop.
If you go the CA glue route, I would encourage you to go to a hobby shop and get a good quality glue. In particular, hobby shops that cater to the RC model airplane crowd will sell a variety of good quality CA glues. Don't get the thick stuff, get something with a thin to medium viscosity. I've noticed in the last several years that lots of no-name Chinese CA glue has been coming on to the market. I've seen evidence that these glues have some impurities in them as evidenced by the fact that they discolor and loose strength after only a few years. A good quality CA glue will not do this.
I'd use some ratcheting bar clamps (harbor freight's work fine - Harbor Freight Tools - Quality Tools at the Lowest Prices ). You can lightly dampen the wood if it is very dry, this will aid the CA glue setting up. You do want to wipe up any excess glue that squeezes out. Acetone will cut CA glue before it sets, (beware though it will probably remove any finish on the wood).