An analytical circuit model able to predict the input impedance of reconfigurable graphene plasmonic dipoles is presented. A suitable definition of plasmonic characteristic impedance, employing natural currents, is used to for consistent modeling of the antenna-load connection in the circuit. In its purely analytical form, the model shows good agreement with full-wave simulations and explains the remarkable tuning properties of graphene antennas. Furthermore, using a single full-wave simulation and scaling laws, additional parasitic elements can be determined for a vast parametric space, leading to very accurate modeling. Finally, we also show that the modeling approach allows fair estimation of radiation efficiency as well. The approach also applies to thin plasmonic antennas realized using noble metals or semiconductors.