A new and distinct cultivar of peach tree, denominated ‘Cardinal Joy’, has firm, melting, semi-freestone fruit with a high coverage of red blush, yellow flesh, normal acidity, rich flavor and pleasant eating quality at maturity. The fruit typically ripen about a week after ‘Flavorich’ (syn. ‘Rich May’) and a few days before ‘Carored’ in mid to late May at Byron, Ga. The tree has self-fertile showy pink flowers and is moderately vigorous and semi-spreading in growth habit. This cultivar has a winter chilling requirement of approximately 850 chill hours, crops well most years, and is suited for high chill areas.