The previously established singlet reference interaction site model (SRISM) theory for the calculation of the fluid structure in the vicinity of a plane impenetrable interface is renormalized for the application to electrical double layers. In combination with the HNC and KH closures, the equations are solved numerically for a IM electrolyte solution adjacent to a charged wall with varying surface charge densities. The wall-solvent and wall-ion density distributions as well as the profiles of the electrical field and the electrical potential are compared to computer simulation results. Reasonable agreement is obtained.