  We present a new method for high precision measurements of polarization
rotation in the frequency range from 0.2 to 2.2 THz using a fiber coupled
time-domain THz spectrometer. A free standing wire-grid polarizer splits THz
light into orthogonal components which are then measured by two separate
detectors simultaneously. We theoretically model the uncertainties introduced
by optical component non-idealities and predict that we may expect to achieve
precisions of order 2.3 $\mu$rad (0.13 mdeg) and accuracies of 0.8$\%$ when
anti-symmetrizing the response with respect to an applied field.
Anti-symmetrization improves precision by more than four orders of magnitude.
We demonstrate this method on a 2D electron gas in magnetic field and show that
we achieve a precision of 20 $\mu$rad (1.1 mdeg) for small polarization
rotation angles. A detailed description of the technique and data analysis
procedure is provided, demonstrating its capability to precisely measure
polarization states in the 0.2 to 2.2 THz range.
