We report on the efficient coupling of terahertz (THz) waves into a dielectric waveguide by means of a diffraction grating engraved at the top of the waveguide. The waveguide is made of a 201-microm-thick high-resistivity silicon wafer. The transmission of the device, measured versus frequency by terahertz time-domain spectroscopy, shows usual m lines when a frequency component of the THz pulse spectrum satisfies the phase-matching condition and is coupled into the waveguide. The experimental data are well modeled with the differential electromagnetic method to compute the diffraction pattern of the grating device. The dispersion curve of the first four modes of propagation is determined from the frequency position of the m lines recorded for different angles of incidence of the THz beam. The waveguide exhibits a weak group velocity dispersion at high frequencies.