The effect of substrate induced spin-orbit (SO) interaction on the transverse dielectric function of a single plane of graphene has been investigated. The Lindhard model approach was then employed to obtain the transverse dielectric function. The dependence of dielectric function on the SO coupling of the graphene sheet with the substrate was theoretically studied. Numerical results show that increasing the Rashba coupling strength results in a blue shift of the van Hove singularities in the linear dielectric response function. Controllable blue shift opens up ways for a variety of device applications
