Nonvolatile and energy-efficient spin-based technologies call for new prospects for realization of logic devices able to operate at terahertz (THz) frequencies. For instance, magnonic elements require an efficient generation of high-energy exchange spin waves at nanometer wavelengths. For this to happen, a substantial coupling of the electro-magnetic stimulus, such as coherent THz field pulses, to the magnon modes is needed. However, the efficient excitation of non-uniform spin waves using THz light is elusive, due to the large momentum mismatch between the millimeter-wave radiation and the exchange-dominated, nanometer-sized, spin waves. Here, we overcome this fundamental problem of light-matter interaction via thin film engineering, exploiting relativistic spin-orbit torques confined to the interfaces of heavy-metal/ferromagnet heterostructures. Using single-cycle broadband THz radiation, we are able to excite spin-wave modes with a frequency of up to 0.6 THz and a wavelength as short as 6 nm. Numerical simulations demonstrate that the coupling of THz light with the exchange-dominated magnons originates solely from interfacial spin-orbit torques. Our results are of general applicability to other magnetic multilayered structures, and offer the prospective of nanoscale control of high-frequency signals.