We present an efficient Schottky-diode detection scheme for Terahertz (THz) radiation, implemented on the material system epitaxial graphene on silicon carbide (SiC). It employs SiC as semiconductor and graphene as metal, with an epitaxially defined interface. For first prototypes, we report on broadband operation up to 580 GHz, limited only by the RC circuitry, with a responsivity of 1.1 A/W. Remarkably, the voltage dependence of the THz responsivity displays no deviations from DC responsivity, which encourages using this transparent device for exploring the high frequency limits of Schottky rectification in the optical regime. The performance of the detector is demonstrated by resolving sharp spectroscopic features of ethanol and acetone in a THz transmission experiment.