In transport models for floating marine litter, such as microplastics, surface wave effects are often included by simply superimposing their Stokes drift (the small net motion of particles induced by surface waves) upon wind-driven Ekman flows and background currents. However, under the joint influence of Earth's rotation and the action of turbulent shear in the upper ocean, surface waves can drive additional Eulerian-mean flows with Ekman-like dynamics. Using buoy data, I show that this wave-induced `Ekman-Stokes' flow must be considered together with the Stokes drift to correctly evaluate the contribution of waves to the transport of floating objects.