We have designed and fabricated a terahertz full-polarimetry instrument, based on control of terahertz polarization in a gas-plasma source, and fast measurement of polarization direction and chirality of the terahertz field in the time-domain without using any external polarizers. We will present details on this new experimental technique including synchronization and calibration of the measurement apparatus against wire-grid polarizers, and derivation of the Jones matrix representation of the propagation optics. The new terahertz time-domain polarimetry (THz-TDP) system extends the polarimetry frequency range to the full bandwidth of gas-plasma sources, and offers accuracy of approximately 1 degrees.