Magnetic properties of nanometer thick Co films intercalated at the graphene/Ir(111) interface are investigated using spin-polarized low-energy electron microscopy (SPLEEM) and Auger electron spectroscopy. We show that the graphene top layer promotes perpendicular magnetic anisotropy in the Co film underneath, even for relatively thick intercalated deposits. The magnetic anisotropy energy is significantly larger for the graphene/Co interface than for the free Co surface. Hybridization of the graphene and Co electron orbitals is believed to be at the origin of the observed perpendicular magnetic anisotropy.