Yes - I've recently made three, two of which were in my wife's Christmas stocking this morning.
As a matter of full disclosure, my wife is more of a knitter than a crocheter, and she hasn't actually used them yet. But I can't believe that what I made won't be functional.
Crochet hooks consist of three basic components - a shaft with a hook at one end, and a handle. I suppose you could make the shaft and handle from different materials. I opted to make everything from a single blank that started out 1" square and about 6 1/2" long. The handle portion can be as simple or as complicated as you want it to be. The shaft portion needs to be about 2 - 2 1/2" long, and the handle is about 4" - but those dimensions aren't rocket science.
The critical factors are the diameter of the shaft, and then shaping of the hook. Crochet hooks are measured in a standard gauge - you can find lots of tables listing shaft diameters for various gauges on the internet. The gauge of the hook determines the size knot that the crocheter makes with the hook. An important point is that the difference between gauges is relatively small - sometimes as little as 0.5mm. Also, it is important that the shaft have essentially a constant diameter over its entire length. My approach to accomplishing that is to turn the shaft to an essentially constant diameter that is about 0.25mm larger than the intended final diameter. Then, I wrap sandpaper around a scrap of plywood and use that to finish the shaft, measuring with a digital caliper until I get to the desired diameter. Wrapping the sandpaper around a scrap of plywood makes it possible to achieve a nearly constant diameter along the length of the shaft. Again, I'm not a crocheter, but my sense is that it's probably good enough to get within 0.1mm of the standard diameter for the intended gauge.
Now the hook. There are a couple of YouTube videos on making crochet hooks, and there was an article in Woodturning Design a few years ago. The approach I take is based on the method that John Lee demonstrates in his video:
https://www.youtube.com/watch?v=fqCshai26Mw. The first step is to taper the end of the shaft to a blunt point. I start the hook by making a cut about halfway through the shaft. Depending on the wood and how brittle it is, I use either a craft knife (box cutter) or a dremel-type tool to make that cut. I use the craft knife to carve the basic hook, and finish it using a fine file to smooth everything.
I finished the hooks I made using pure tung oil - two applications, fat over lean. Two were made from white oak, while the third was made from bloodwood.
Some gauges involve very small shafts - so small that I would be concerned about whether turned wood would have enough strength. I suppose that if you needed to make a very small gauge crochet hook, you could always take a commercial metal shaft/hook and mount it in a shop-made shaft.
