We experimentally observe Floquet Raman transitions in the weakly driven solid state spin system of nitrogen-vacancy center in diamond. The periodically driven spin system simulates a two-band Wannier-Stark ladder model, and allows us to observe coherent spin state transfer arising from Raman transition mediated by Floquet synthetic levels. It also leads to the prediction of analog photon-assisted Floquet Raman transition and dynamical localisation in a driven two-level quantum system. The demonstrated rich Floquet dynamics offers new capabilities to achieve effective Floquet coherent control of a quantum system with potential applications in various types of quantum technologies based on driven quantum dynamics. In particular, the Floquet-Raman system may be used as a quantum simulator for the physics of periodically driven systems.