Spin-momentum locking is a universal wave phenomenon promising for applications in electronics and photonics. In acoustics, Lord Rayleigh showed that surface acoustic waves exhibit a characteristic elliptical particle motion strikingly similar to spin-momentum locking. Although these waves have become one of the few phononic technologies of industrial relevance, the observation of their transverse spin remained an open challenge. Here, we observe the full spin dynamics by detecting ultrafast electron cycloids driven by the gyrating electric field produced by a surface acoustic wave propagating on a slab of lithium niobate. A tubular quantum well wrapped around a nanowire serves as an ultrafast sensor tracking the full cyclic motion of electrons. Our acousto-optoelectrical approach opens previously unknown directions in the merged fields of nanoacoustics, nanophotonics, and nanoelectronics for future exploration.