We report on angle-resolved photoemission studies of the electronic pi states of high-quality epitaxial graphene layers on a Ni(111) surface. In this system the electron binding energy of the pi states shows a strong dependence on the magnetization reversal of the Ni film. The observed extraordinarily large energy shift up to 225 meV of the graphene-derived pi band peak position for opposite magnetization directions is attributed to a manifestation of the Rashba interaction between spin-polarized electrons in the pi band and the large effective electric field at the graphene/Ni interface. Our findings show that an electron spin in the graphene layer can be manipulated in a controlled way and have important implications for graphene-based spintronic devices.