It has been debated for decades whether rigid inclusions, such as porphyroclasts and porphyroblasts, do or do not rotate in a softer matrix during deformation. Experiments and numerical simulations with viscous matrix rheologies show ongoing rotation of circular inclusions, whereas using Mohr-Coulomb plasticity results in nonrotation. Because the rocks in which inclusions are found normally undergo deformation by dislocation creep, we applied a full-field crystal plasticity approach to investigate the rotation behavior of rigid circular inclusions. We show that the inclusion's rotation strongly depends on the anisotropy of the matrix minerals. Strongly anisotropic minerals will develop shear bands that reduce the rotation of inclusions. Inhibition of rotation can only occur after a significant amount of strain. Our results may help to explain why geologic rigid objects often show evidence for rotation, but not necessarily in accordance with the viscous theory that is usually applied to these systems.