At the graphene-electrolyte interface, the polarizability of both the surface and the solution plays a major role in defining the interfacial structure and dynamics of the ions. Current molecular models predict different ion adsorption behavior at the interface depending on whether surface or solution polarization is included in the model. Here, we propose a simple method to parametrize the ion-carbon interaction from density functional theory, implicitly modeling the solution using the conductor-like polarizable continuum model. The new model simultaneously takes into account the polarizability of both the graphene sheet and the solution without the need to use time-consuming polarizable potentials and can predict the ion adsorption trend so far only achievable using first-principles simulations. Simulations performed with 1 M electrolyte solutions of different ions show that cations are strongly adsorbed onto the graphene surface with a trend (Li+ < Na+ < K+) opposite to that predicted by the gas-phase calculations and different from that obtained from the single-ion simulations.