1/256 microstepping stepper motor
Do you want the good news first, or the bad?

The bad news is that what you are asking for is not available.

The good news is that what you need (rather than what you asked for) is available. On eBay. It's called a "motorized rotary stage". An example would be this unit, which has a data sheet here, although the unit for sale is apparently an older unit which does not exactly correspond to the data sheet. At a guess, though, it will do much better than you need.

And eBay has a lot of this sort of unit. Of course, as in this case they are often old, unsupported, and you'll have to learn how to work with proprietary interfaces.

If you're more adventurous (that is, wealthy), various companies such as Thorlabs and Newport will gladly sell you new units much better than you need. Well, and almost certainly more expensive than you can afford, but you didn't set price limits in your question.