Local perturbations in the relative orientation of the magnetic moments in a continuous magnetic system can propagate in the form of waves. These so-called spin waves represent a promising candidate as an information carrier for spin-based low-power applications. A localized, energy-efficient excitation of coherent and short-wavelength spin waves is a crucial technological requirement, and alternatives to excitation via the Oersted field of an alternating current must be explored. Here, we show how a domain wall pinned at a geometrical constriction in a perpendicularly magnetized thin nanowire emits spin waves when forced to rotate by the application of a low direct current flowing along the wire. Spin waves are excited by the in-plane stray field of the rotating domain wall and propagate at an odd harmonic of the domain wall rotation frequency in the direction of the electron's flow. The application of an external field, opposing domain wall depinning induced by the current, breaks the symmetry for spin wave propagation in the two domains, allowing emission in both directions but at different frequencies. The results presented define a new approach to manufacture tuneable high-frequency spin wave emitters of easy fabrication and low power consumption.