We present a new instrumentation and calibration procedure for terahertz time-domain spectroscopic ellipsometry (THz-TDSE) that is a newly established characterization technique. The experimental setup is capable of providing arbitrary angle of incidence in the range of 15°-85° in the reflection geometry, and with no need for realignment. The setup is also configurable easily into transmission geometry. For this setup, we successfully used hollow core photonic band gap fiber with no pre-chirping in order to deliver a femtosecond laser into a THz photoconductive antenna detector, which is the first demonstration of this kind. The proposed calibration scheme can compensate for the non-ideality of the polarization response of the THz photoconductive antenna detector as well as that of wire grid polarizers used in the setup. In the calibration scheme, the ellipsometric parameters are obtained through a regression algorithm which we have adapted from the conventional regression calibration method developed for rotating element optical ellipsometers, and used here for the first time for THz-TDSE. As a proof-of-principle demonstration, results are presented for a high resistivity silicon substrate as well as an opaque Si substrate with a high phosphorus concentration. We also demonstrate the capacity to measure a few micron thick grown thermal oxide on top of Si. Each sample was characterized by THz-TDSE in reflection geometry with different angle of incidence.