The presence of waves exposes tidal stream turbines to large and cyclic hydrodynamic loads which significantly influence the design requirements for tidal turbine blades. Here we describe a loading phenomenon not previously considered in literature caused as blades rotationally sample an oscillating and vertically decaying wave-induced velocity field. Although implicitly incorporated into numerical models, the dominant causes and relative influence have not previously been considered. In this article this effect is described through theoretical analysis and validated through scaled experiments; including irregular waves at angles to the rotor and current field. The associated loads are found to be strongly correlated to the wavenumber. The nature of the rotational-sampling-effect is confirmed through analysis of the experimental results, where characteristic sidebands are effectively predicted in the blade root bending moment spectra. It is estimated to account for between 8% and 16% of the fatigue damage and between 7% and 13% of the peak root bending moment for the conditions tested. A key finding is that two bilaterally-symmetrical oblique wave conditions do not produce equivalent loading patterns: one produces higher frequency oscillations. Additionally, it is found that the frequency of these loads reduces linearly with rotational speed; highlighting another consideration for tidal stream turbine operation.