Spectroscopy and imaging in the terahertz (THz) region of the electromagnetic spectrum has proven to provide important insights in fields as diverse as chemical analysis, materials characterization, security screening, and nondestructive testing. However, compact optoelectronics suited to the most powerful terahertz technique, time-domain spectroscopy, are lacking. Here, we implement single GaAs nanowires as microscopic coherent THz sensors and for the first time incorporated them into the pulsed time-domain technique. We also demonstrate the functionality of the single nanowire THz detector as a spectrometer by using it to measure the transmission spectrum of a 290 GHz low pass filter. Thus, nanowires are shown to be well suited for THz device applications and hold particular promise as near-field THz sensors.