I don't see as there's any need for any great speed?, you're sending data to a stepper motor, which is an exceptionally slow device.
The easiest way do USB is to use a USB/Serial converter, so your PC program accesses the interface as a simple serial port, and your processor connects via a serial link to the converter.
Alternatively you could use a processor that has it's own USB interface, but this is much more complicated.
Any PIC (or other micro-controller) would be able to easily handle such a simple task. Where before your PC program actually controlled the stepper, now the PIC controls the stepper - you simply send it instructions, and it carries them out (something like L45 - for 45 steps left?).