We report on a time-domain polarimetry (TDP) system for generating and detecting broadband terahertz (THz) waves of different polarization angles. We generate THz waves from two-color laser filaments and determine their polarization states with a detection bandwidth of up to 8 THz using a spinning gallium phosphide crystal. The polarization of THz emission can be controlled by adjusting the position and tilt angle of the β-barium borate crystal. We characterize the precision of this system for polarimetric measurements at fixed time delay to be and for complete time-domain waveforms. We also demonstrate the feasibility of our TDP system by measuring broadband optical properties of anisotropic samples in both transmission and reflection geometries. The THz-TDP technique can be easily integrated in conventional THz time-domain spectroscopy setups using nonlinear crystal detectors.