How would I model hysteresis? I have the task of modeling the current to torque mapping for a given motor. I have an experimental set up where I can retrieve current, torque pairs.

Now my initial approach was to model the relationship with a regression curve, but I realized that the motor certainly shows some kind of hysteresis.

How would I be able to compute a current to torque mapping that also includes hysteresis from the data I obtained
If your goal is solely predicting torque for a given engine, you can ignore hysteresis. A regression model will implicitly model hysteresis in the learned parameters of the model.

If your goal is building a model hysteresis for a given motor, then you should systematically measure performance with different recent histories. Then apply a time series model to model the effect of recent history.