Efficient manipulation of magnetic order with electric current pulses is desirable for achieving fast spintronic devices. The Rashba-Edelstein effect, wherein spin polarization is electrically induced in noncentrosymmetric systems, provides a mean to achieve staggered spin-orbit torques. Initially predicted for spin, its orbital counterpart has been disregarded up to now. Here we report a generalized Rashba-Edelstein effect, which generates not only spin polarization but also orbital polarization, which we find to be far from being negligible. We show that the orbital Rashba-Edelstein effect does not require spin-orbit coupling to exist. We present first-principles calculations of the frequency-dependent spin and orbital Rashba-Edelstein tensors for the noncentrosymmetric antiferromagnets CuMnAs and Mn[Formula: see text]Au. We show that the electrically induced local magnetization can exhibit Rashba-like or Dresselhaus-like symmetries, depending on the magnetic configuration. We compute sizable induced magnetizations at optical frequencies, which suggest that electric-field driven switching could be achieved at much higher frequencies.