SuperTuxKart uses SDL2 to recognize gamepads, and a Xbox controller should normally work fine.
You can open a ticket on our official bug tracker, providing as many details as possible about how the issue manifests: https://github.com/supertuxkart/stk-code/issues
It can be quite difficult to pinpoint what is going wrong without the problematic setup directly in hand, but maybe we can figure it out.
Also note that you aren't forced to play on mobile if your gamepad is giving you trouble, keyboard controls work very well for STK.