  Commensurable twisted bilayers can drastically change the magnetic properties
of chromium trihalide layered compounds, which opens novel opportunities for
tuning magnetic states through layer rotations. Here, we introduce a
mathematical approach to obtain moir\'e patterns in twisted hexagonal bilayers
by performing a certain commensurable rotation $\theta$ over one layer. To test
our approach, we apply it to find moir\'e structures with
$\theta=21.79^{\circ}$ and $32.20^{\circ}$ in the phases R$\bar{3}$ and C2/m of
CrI$_{3}$. For comparison purposes, we also consider a non-shifted CrI$_{3}$
structure. Electronic and magnetic properties of the so-obtained systems are
computed by \textit{Ab-Initio} methodologies. Results show the presence of
rotation-angle-dependent magnetic configurations and steep modifications of the
dispersion bands due to variations in the nearest and next nearest distances
among layers of Cr atoms. Modifications obtained from these commensurable
rotations are discussed on the basis of competition among different energy
contributions due to changes in the atomic arrangements.
