Yes. We most likely can fix it. We fix these breaks all the time.
How much? $50 and up. Something like this will run you about $150, though:
The most common neck breaks we see are on Gibson and Epiphone instruments. This has to do with the design of the headstock. It tilts back across the end-grain of the wood. Many of these necks are mahogany, and that is a soft wood. If you own a guitar with this type of headstock, please be extra careful not to drop it. Don't even drop it in the case! We can repair 98% of them, but it will kill the resale value of your instrument. It also leaves you with scars that can only be hidden by repainting. (an expensive and time consuming process)
Don't throw that broken guitar in the dumpster. Bring it in and we'll see what we can do to save it.