Understanding how floating particles are transported by streaming waters is crucial in predicting the transport of plastic pollution, which is dramatically abundant in rivers, lakes, and oceans. Using particle tracking velocimetry, we investigate the motion of floating particles of different shape and size on the turbulent free surface of a field-scale meandering stream. We consider two different locations, in both of which the role of surface waves on transport is deemed negligible. Millimetre-sized spheres are used as tracers to characterize the surface flow. These are compared with centimetre-sized discs and rods, approximating typical-sized pieces of floating litter. The larger particles exhibit similar mean and fluctuating velocities as the tracers but filter out the extreme turbulent accelerations. Consequently, their motion is more time-correlated and their spreading rate is larger. This behaviour is also confirmed by complementary laboratory measurements in an open channel flow. The rotation of the rods, affected by a range of turbulent scales, reduces the correlation time scale of their translational motion, and leads to a slower dispersion compared to the discs, despite the rods’ length being larger than the discs’ diameter. Taken together, these results indicate that the motion of finite-sized objects floating on the surface of weakly wavy turbulent waters is consistent with the behaviour of inertial particles in three-dimensional turbulence. These results can be valuable when constructing predictive models of floating plastics.