Deformation of granular materials is often characterized by strain localization in the form of shear bands, which exhibit a characteristic width of about 10–20 particle diameters. Much of the relative motion of particles within a shear band is accompanied by rolling, as opposed to sliding, since the latter requires more dissipative work. However, in a densely packed assembly, rolling cannot be accomplished without some sliding. This dissipative constraint implies a characteristic rotation transmission distance, i.e., the distance to which the information about rotation of a particle propagates. Here, we use the discrete element method to investigate this length and its directional dependence as function of the force chain network. We found that the rotation transmission distance correlates with the shear band width observed in experiments and previous numerical simulations. It is strongly dependent on the particle size distribution and the coefficient of interparticle friction, and weakly dependent on pressure. Moreover, the transmission of rotations is strongly directionally dependent following the pattern of force chains. To describe this dependence, we define a nonlocal tensorial description of force chain directionality.