  We find unusually large cross-polarized (and anti-symmetric) Raman signature
of A$_{\rm g}$ phonon mode in CrI$_3$, in agreement with experiments. The
signal is present only when the following three effects are considered in
concert: ferromagnetism on Cr atoms, spin-orbit interaction, and resonant
effects. Somewhat surprisingly, we find that the relevant spin-orbit
interaction potential originates from iodine atoms, despite magnetism being
mostly on chromium atoms. We analyze the Raman signature as a function of
magnetic order, the direction of the magnetic moment, energy and polarization
of light used for Raman scattering, as well as carrier lifetime. In addition to
a strong cross-polarized Raman signal, we also find unusually strong phonon
modulated magneto-optical Kerr effect (MOKE) in CrI$_3$.
