Many stepper motor driver ICs do a lot more than provide a high current output stage per coil or coil end as Bruce just described. Its common to have pulse and direction inputs, where pulse causes it to step once on each activation, and direction is a logic level that chooses whether the step is forward or backwards. Also, for a star tracker, you only need a fixed speed in tracking mode, with that speed determined by the mount's gearing, so you can calculate the exact pulse rate required and generate it in pure dumb logic by dividing down the output of a crystal oscillator, to whatever accuracy you require.
However, as has been pointed out, that would be actually the *HARD* way compared to using an Arduino clone*, and a stepper driver shield. That would also let you compensate for the tangent error of the mount electronically, for optimum tracking accuracy over the full mechanical movement range.
If you need a menu interface, add an I2C LCD and button shield, but the application is simple enough that once the speed is worked out, all the user interface you need would be a stop/run switch and a status LED.
Also most USB powerbanks shut down at low load currents, so you may well need to use a LiPO with a separate 5V output boost board.
* Genuine Arduinos use a ceramic resonator for the ATmega clock. The accuracy and thermal stability is poor compared to a crystal, so in timekeeping applications that don't justify the use of external RTC, a clone that uses a 16MHz crystal rather than a resonator is preferable.