The growth of semiconductor nanowires (NWs) has recently opened new paths to silicon integration of device families such as light-emitting diodes, high-efficiency photovoltaics, or high-responsivity photodetectors. It is also offering a wealth of new approaches for the development of a future generation of nanoelectronic devices. Here we demonstrate that semiconductor nanowires can also be used as building blocks for the realization of high-sensitivity terahertz detectors based on a 1D field-effect transistor, configuration. In order to take advantage of the low effective mass and high mobilities achievable in III-V compounds, we have used InAs nanowires, grown by vapor-phase epitaxy, and properly doped with selenium to control the charge density and to optimize source drain and contact resistance. The detection mechanism exploits the nonlinearity of the transfer characteristics: the terahertz radiation field is fed at the gate-source electrodes with wide band antennas, and the rectified signal is then read at the output in the form of a DC drain voltage. Significant responsivity values (>1 V/W) at 0.3 THz have been obtained with noise equivalent powers (NEP) < 2 x 10(-9) W/(Hz)(1/2) at room temperature. The large existing margins for technology improvements, the scalability to higher frequencies, and the possibility of realizing multipiixel arrays, make these devices highly competitive as a future solution for terahertz detection.