The shear-induced self-organization of active rotors into stripy aggregates is studied by carrying out computational simulations. The rotors, modeled by monolayers of frictional spheres, develop to stripy microstructures only when they counterrotate with respect to the vorticity of the imposed shear flow. The average width of the stripes is demonstrated to be linearly dependent on the relative intensity of active torque to the shear rate. By giving insight into three collective particle behaviors, i.e., shear-induced diffusion, rotation-induced rearrangement, and edge flows, we explain the mechanisms of formation of the particle stripes. Additionally, the rheological result shows the dependence of shear and rotational viscosities on the active torque direction and the oddness of the normal stress response. By exhibiting a collective phenomenon of active rotors, our study paves the way to understanding chiral active matter.