We present a universal polarization terahertz (THz) phase controller using a randomly aligned liquid crystal (LC) cell with graphene electrodes. The LC cell was fabricated using a nematic LC and two quartz substrates that were coated with a monolayer of graphene as the transparent electrode. The LC in the cell was prepared without any alignment treatments and was randomly aligned. The size of the random domains and the width of the disclination lines in the LC layer were several tens of microns. These textures disappeared when an alternating voltage was applied to the LC through the graphene layers. Using a THz time domain spectroscopic technique, we investigated the complex transmittance of the LC cell. The LC cell was highly transparent in the THz frequency range, and there was little change in the transmittance with the applied voltage. This indicated that the scattering loss originating in the randomly aligned LC molecules was small for the THz waves. We also demonstrated that the THz phase shift could be controlled by the applied voltage. The amplitude of the phase shift was explained by the ordinary and extraordinary refractive indices of the LC. These LC cells with graphene electrodes can be used to realize universal polarization THz phase controllers because of the random alignment.