The recent discovery that resonant inelastic x-ray scattering can probe single-magnon (SM) dispersions in transition metal (TM) oxides when the x-ray energy is tuned to the TM L edge has put this technique on a par with inelastic neutron scattering. It is generally presumed that selection rules forbid SM scattering at oxygen (O) K edges. However, based on a symmetry analysis and exact diagonalization study, we show that SM scattering at O K edges becomes allowed when (i) spin-orbit coupling is present in the TM d shell and (ii) inversion symmetry at the O site is broken. For cuprates the resulting SM amplitude is very weak, but in iridates both prerequisites can amply be fulfilled.