This paper investigated the cyclic response of a new viscoelastic damper that utilized a rotational mechanism to enhance shear deformation in the viscoelastic material and increase its energy dissipation. Three damper prototypes were fabricated and subjected to displacement-controlled cyclic excitations with varying strain amplitudes and frequencies. For comparison, three conventional viscoelastic dampers, each containing an equivalent volume of viscoelastic material to the proposed damper, were also fabricated and tested. Results indicated that the proposed damper had up to three times larger loss factor and five times larger damping coefficient than the tested conventional viscoelastic damper. This study also presented two analytically driven equations to estimate the proposed damper's rotational stiffness and damping coefficient. A finite element model was proposed for simulating the damper in software, and its effectiveness was demonstrated.