Parts of my skin are not tanning like the rest. Does a ringworm rash change skin pigment?

Yes. Often, ringworm, a type of fungal infection will cause the skin to be hypopigmented so the area where you have the infection will be lighter. Try applying an antifungal cream. Once the infection clears, the skin color should return to normal.
Yes, but. Ringworm (tinea corporis) can affect tanning during an acute infection and during heling, but once healed, the skin tanning should return to normal.