The RF performance of a nanoelectromechanical systems (NEMS) capacitive switch based on graphene is evaluated. Our results show that graphene can be a good candidate for the membrane of RF NEMS switches in applications where low actuation voltage and fast switching are required. The conductivity of the membrane is accurately modeled in the up-and down-state positions of the switch by considering the field effect of graphene. Rigorous full-wave simulations are then performed to obtain the scattering parameters of the switch. It is shown that graphene's conductivity variation due to electric field effect has a limited yet beneficial impact on the performance of the switch. It is also demonstrated that while monolayer graphene results in quite high switch losses at high frequency, the use of multilayer graphene, can considerably reduce the switch losses and improve the RF performance. Finally, an equivalent circuit model for the graphene-based RF NEMS switch is extracted and the results are compared with the full-wave 3-D electromagnetic simulation. These results motivate further efforts in the fabrication and characterization of graphene RF NEMS.