How to make a concrete stain from Georgia’s red clay?

Yes the iron oxide in Georgia red clay will stain concrete. I don't think just raw clay would be fully absorbed by the concrete especially if it was smoothed and sealed. It might absorb more into wet or fresh cement like fresco painting. experiment on a couple cheap pavers or stepping stones. Try rubbing and scrubbing the watered down clay slip into the cement then rinsing and sealing when dry . Or take dried and powdered clay and mixing it into the sealer then painting the stone.Commercial stains might be easier and more predictable.

Red Clay will really stain your clothes. Use a rust remover like Wink. Don't use the dryer because heat sets in stains.