Efficient manipulation of magnetic order with electric current pulses is desirable for achieving fast spintronic devices. The Rashba-Edelstein effect, wherein a spin polarization is electrically induced in noncentrosymmetric systems, provides a mean to achieve current-induced staggered spin-orbit torques. Initially predicted for spin, the orbital counterpart of this effect has been disregarded up to now. Here, we present a generalized Rashba-Edelstein effect, which generates not only spin polarization but also orbital polarization, which we find to be far from being negligible and could play a crucial role in the magnetization dynamics. We show that the orbital Rashba-Edelstein effect does not require spin-orbit coupling to exist. We present first-principles calculations of the frequencydependent spin and orbital Rashba-Edelstein susceptibility tensors for the noncentrosymmetric antiferromagnets CuMnAs and Mn2Au. We show that the electrically induced local magnetization has both staggered in-plane components and non-staggered out-of-plane components, and can exhibit Rashba-like or Dresselhaus-like symmetries, depending on the magnetic configuration. Furthermore, there is an induced local magnetization on the nonmagnetic atoms as well, that is smaller in Mn2Au than in CuMnAs. We compute sizable induced magnetizations at optical frequencies, which suggest that electric-field driven switching could be achieved at much higher frequencies.arXiv:1905.08279v1 [cond-mat.mtrl-sci]