We propose a Stokes polarimetry system containing a twisted hybrid aligned nematic (HAN) liquid crystal (LC) cell as a simple and compact polarimetry setup that can function without any mechanical movement of the optical components. We measured the Mueller matrix of the twisted HAN-LC cell and compared it with the Mueller matrix of an ordinary nontwisted HAN-LC cell with respect to practicability for the proposed LC polarimetry system. The basic measurement principle of LC polarimetry is presented after determining the best set of four driving voltages for maximizing measurement performance. Finally, we conducted some demonstrative experiments using two different birefringent samples to ensure the applicability of the proposed LC polarimetry system.