In this paper we study the current-induced spin polarization in a two-dimensional electron gas, known also as the Edelstein effect. Compared to previous treatments, we consider both the Rashba and Dresselhaus spin-orbit interaction as well as the spin-orbit interaction from impurity scattering. In evaluating the Kubo formula for the spin polarization response to an applied electric field, we explicitly take into account the side-jump and skew-scattering effects. We show that the inclusion of side-jump and skew-scattering modifies the expression of the current-induced spin polarization.