We develop a molecular theory of aqueous electrolyte solution sorbed in a nanoporous carbon aerogel electrode, based on the replica reference interaction site model (replica RISM) for realistic molecular quenched-annealed systems. We also briey review applications of carbon aerogels for supercapacitor and electrochemical separation devices, as well as theoretical and computer modelling of disordered porous materials. The replica RISM integral equation theory yields the microscopic properties of the electrochemical double layer formed at the surface of carbon aerogel nanopores, with due account of chemical specicities of both sorbed electrolyte and carbon aerogel material. The theory allows for spatial disorder of aerogel pores in the range from micro- to macroscopic size scale. We considered ambient aqueous solution of 1 M sodium chloride sorbed in two model nanoporous carbon aerogels with carbon nanoparticles either arranged into branched chains or randomly distributed. The long-range correlations of the carbon aerogel nanostructure substantially affect the properties of the electrochemical double layer formed by the solution sorbed in nanopores.