We propose and develop a classical density functional theory for the description of a minor amount of water dissolved in ionic liquid in the vicinity of an electrode. In addition to the electrostatic energy and lattice-gas mixing entropy terms, the utilised grand canonical potential contains several phenomenological terms/parameters that describe short-range interactions between ions, water molecules and the electrode. Here we investigate: (i) specific interaction of ions and molecules with the electrode, which are responsible for their specific adsorption; (ii) hydrophilicity/hydrophobicity of ions. We obtain water electrosorption isotherms as a function of the potential drop across the electrical double layer, investigate its asymmetry with respect to the sign of electrode potential, and establish the relationship between the sign of this asymmetry and hydrophobicity/hydrophilicity of cations and anions. We also calculate the effect of water electrosorption on the double layer differential capacitance which brings clear new features to its voltage dependence, some of which have been already experimentally observed. (C) 2018 Published by Elsevier Ltd.