Terahertz radiation encompasses a wide band of the electromagnetic spectrum, spanning from microwaves to infrared light, and is a particularly powerful tool for both fundamental scientific research and applications such as security screening, communications, quality control, and medical imaging. Considerable information can be conveyed by the full polarization state of terahertz light, yet to date, most time-domain terahertz detectors are sensitive to just one polarization component. Here we demonstrate a nanotechnology-based semiconductor detector using cross-nanowire networks that records the full polarization state of terahertz pulses. The monolithic device allows simultaneous measurements of the orthogonal components of the terahertz electric field vector without cross-talk. Furthermore, we demonstrate the capabilities of the detector for the study of metamaterials.