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, a mathematical approach to obtain moiré patterns in twisted hexagonal bilayers by performing a certain commensurable rotation θ over one layer is presented. To test the approach, moiré structures with (Formula presented.) and 32.20° in the phases R (Formula presented.) and C2/m of CrI3 are obtained via the related methodology. For comparison purposes, a non-shifted CrI3 structure is also considered. Electronic and magnetic properties of the so-obtained systems are computed by 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 neighborhood. © 2022 Wiley-VCH GmbH