A different type of Casimir-type interaction is theoretically predicted: a single-interface torque at a junction of an anisotropic material and a vacuum or another material system. The torque acts to reorient the polarizable microscopic units of the involved materials near the interface, and thus to change the internal structure of the materials. The single-interface torque depends on the zero-point energy of the interface localized and extended modes. Our theory demonstrates that the single-interface torque is essential to understand the Casimir physics of material systems with anisotropic elements and may influence the orientation of the director of nematic liquid crystals.