How long does it take for scalp ringworms to clear up after you start taking the medication?

2-3 weeks: Treatment for ringworm can take two to three weeks to show significant improvement. Any associated hair loss can take longer to grow back.

Quite a while: Compared to many other infections these are a longer investment of time and effort. The germ has gone deep into the hair follicles and require oral medication to reach/eliminate. Difficult cases can take a month or more of medication for final cure. Topical medications can sometimes provide a cosmetic benefit at the level of exposed skin, but won't cure it alone.