Statistically associating fluid theory (SAFT) provides closed-form free energies by perturbation methods. We propose here a SAFT equation of state for ionic liquids that models the contribution from Coulomb forces after that of the Restricted Primitive Model (RPM) in the Mean Spherical Approximation (MSA). The resulting SAFT-MSA equation, fitted to simulated orthobaric curves of imidazolium based ionic liquids, predicts experimental density data with errors approximate to 1% and the characteristic decrease of all critical coordinates with increasing cation size. The SAFT-MSA equation can be applied to calculate thermodynamic coefficients, the speed of sound and surface tension (among other properties) of pure ionic liquids and can be generalized straightforwardly to mixtures.