  We present a numerical simulation of the X-ray magnetic circular dichroism
(XMCD) at the $L_{2,3}$ edge of Mn in altermagnetic MnF$_2$ using a combination
of density functional + exact diagonlization of an atomic model. We explore how
the dichroic spectra vary with the light propagation vector and the N\'eel
vector. We show how XMCD in rutile structures can be employed to determine the
orientation of the N\'eel vector. An exact relationship between the XMCD
spectra for different orientation of the N\'eel vector valid in the absence on
the valence spin-orbit coupling and core-valence multipole interaction is
derived and its approximate validity demonstrated by numerical calculation for
the full Hamiltonian.
