A rich class of spintronics-relevant phenomena require implementation of robust magnetism and/or strong spin-orbit coupling (SOC) to graphene, but both properties are completely alien to it. Here, we for the first time experimentally demonstrate that a quasi-freestanding character, strong exchange splitting and giant SOC are perfectly achievable in graphene at once. Using angle- and spin-resolved photoemission spectroscopy, we show that the Dirac state in the Au-intercalated graphene on Co(0001) experiences giant splitting (up to 0.2 eV) while being by no means distorted due to interaction with the substrate. Our calculations, based on the density functional theory, reveal the splitting to stem from the combined action of the Co thin film in-plane exchange field and Au-induced Rashba SOC. Scanning tunneling microscopy data suggest that the peculiar reconstruction of the Au/Co(0001) interface is responsible for the exchange field transfer to graphene. The realization of this "magneto-spin-orbit" version of graphene opens new frontiers for both applied and fundamental studies using its unusual electronic bandstructure.