  We present numerical simulation of the X-ray magnetic circular dichroism
(XMCD) of the $L_{2,3}$ and $M_{2,3}$ edges of Ru in antiferromagnetic RuO$_2$
using a combination of density functional + dynamical mean-field theory and
configuration interaction treatment of Anderson impurity model. We study the
dependence of the dichroic spectra on the orientation of the N\'eel vector and
discuss it in the context of altermagnetism. Approximate equivalence between
the XMCD spectra for geometries with X-rays propagating parallel and
perpendicular to the N\'eel vector is found and shown to be exact in absence of
valence spin-orbit coupling and core-valence multipolar interaction.
