An ideally polarizable cation-selective solid particle is suspended in an electrolyte solution and is exposed to a uniformly applied ambient electric field. The electrokinetic transport processes are described in a closed mathematical model, consisting of differential equations, representing the physical balance laws, as well as boundary conditions and integral constraints, representing the physicochemical condition on the particle boundary and at large distances away from it. Solving this model would in principle provide the electro-kinetic flow about the particle and the concomitant particle drift relative to the otherwise quiescent fluid. Using matched asymptotic expansions, the model is analyzed in the thin-Debye-layer limit. An effective `macroscale' description is extracted, whereby effective boundary conditions represent appropriate asymptotic matching with the Debye-scale fields. The macroscale description significantly differs from that corresponding to a chemically inert ideally polarizable particle. Thus, ion selectivity on the particle surface results in a macroscale salt concentration polarization, whereby the electric potential is rendered non-harmonic. Moreover, the uniform Dirichlet condition governing this potential on the particle surface is transformed into a non-uniform Dirichlet condition on the macroscale particle boundary. The Dukhin--Derjaguin slip formula still holds, but with a non-uniform zeta potential that depends upon the salt concentration distribution. For weakly applied fields, an approximate solution is obtained as a perturbation to an equilibrium state. The linearized solution corresponds to a uniform zeta potential; it predicts a particle velocity which is proportional to the applied field. The associated electrokinetic flow differs however from that in the comparable electrophoresis of an inert particle surface, since it is driven by two different agents, electric field and salinity gradients, which are of comparable magnitude. The velocity field, specifically, is rotational.