Spin waves (SWs) and domain walls (DWs) have been two prominent research fields in the history of magnetism, which remain active in unfolding spintronics. In the past decades, rich novel dynamic effects have been revealed in the exploration of SWs and DWs in magnetic nanostructures, promising important applications in new-generation magnetic devices. Due to the absence of Joule heat, SWs are considered as candidates for information carriers with ultra-low power consumption. DW dynamics at the nanoscale, besides its fundamental interests, also bears significance in terms of technology applications. A spin nano-oscillator is a new type of spintronic device, which has advantages such as small size, wide frequency modulation range, and easy integration compared to traditional semiconductor oscillators. Former spin nano-oscillators are usually driven by spin polarized electric current via the so-called spin-transfer torque effect. In a typical spin nano-oscillator, the magnetization of the free layer of a spin valve (SV) or a magnetic tunneling junction (MTJ) is driven by electric currents to sustain a continuous precession, with the damping of the system compensated by the current. Highly tunable microwave signals can be generated during the oscillation. In a current-driven DW nano-oscillator proposed recently, the free layer of a SVor MTJ is replaced by a transverse DW pinned in a ferromagnetic nanowire, which oscillates periodically subject to a spin-transfer torque exerted by a current passing through the DW. It has been pointed out that SWs also carry spin currents and thus spin angular momentum, which can as well be transferred to local magnetic structures, such as DWs, during its transportation. This effect is referred to as the magnonic spin-transfer torque. Previous studies have been focused on ferromagnetic thin-films, in which a translational motion of the DW is found to be induced by the electric current. In this work, we study the SW-driven DW dynamics in cylindrical nanowires. If thin enough, a stable transverse DW can form in a ferromagnetic nano-cylinder. We demonstrate by micromagnetic simulations that when the DW is pinned by a geometric means, a transmitting SW gives rise to a rotational motion instead of a translational one to the DW. The direction of the DW rotation relies on its type (head-to-head or tail-to-tail) and the propagation direction of the SW. The DW precession frequency is found to be positively dependent on the SW amplitude and negatively dependent on the damping parameter of the system. Based on the magnonic spin-transfer torque effect, we present an analytical model, which yields quantitative agreements with our numerical results. It was predicted in the model that the DW precession frequency contains rich information about the propagating SWs, such as the transmission rate, amplitude and propagating velocity. Therefore, our result in principle provides a new approach for the detection and measurement of propagating SWs in ferromagnetic nanostructures. The DW precession frequency observed in our system is in the GHz regime. Our results thus also propose a possible design scheme for a magnonic spin-transfer torque microwave nano-oscillator.