The rotational spectrum of thiocyanic acid HSCN, a highly polar isomer of the well-known astronomical molecule isothiocyanic acid HNCS, has been measured in two radio bands: in the centimeter-wave band by Fourier transform microwave spectroscopy in a molecular beam, and in the millimeter-wave band by long-path absorption spectroscopy in a low-pressure glow discharge. Twelve spectroscopic constants were derived from more than 60 a-type rotational transitions between 11 and 346 GHz with J up to 30 and Ka <= 6, including seven centimeter-wave transitions with resolved hyperfine structure. With these constants the rotational spectrum in the Ka = 0 and Ka = 1 ladders—those most likely to be observed in space—can now be calculated up to 400 GHz with formal uncertainties of less than 0.2 km s-1 in equivalent radial velocity. Thiocyanic acid was recently identified in Sgr B2 by Halfen et al. following the laboratory measurements, and there is possible evidence for it in cold dark clouds, with the implication that HSCN may be detectable in many galactic sources.