Graphene integration with commonly used Si is very promising for high-performance devices in the future. The fabrication of Si on graphene has gained more attention to realize promising device design and to develop high-quality Si thin-film technology. Nevertheless, attempts to develop Si on graphene are very few, and films are often of poor-quality. Introducing an AlN atomic layers as an interface layer, this paper reports the growth of single crystalline Si on graphene using radio-frequency plasma-assisted molecular beam epitaxy (RF-MBE). We focus on the initial growth process of Si on graphene and clarify the epitaxial relationship between Si and graphene. It is observed that the initial Si nuclei rotate randomly on the surface if deposited directly on the graphene, which implies that orientation control of the initial Si layers on the epitaxial graphene is very important to obtain high-quality layers. The proposed thin AlN intermediate layer to the graphene surface greatly enhances the orientation of initial Si nuclei and results in a single crystalline Si layer on the epitaxial graphene.