In this paper we study the wall pressure and vorticity fields of the Stokes boundary layer in the intermittently turbulent regime through direct numerical simulation (DNS). The DNS results are compared to experimental measurements and a good agreement is found for the mean and fluctuating velocity fields. We observe maxima of the turbulent kinetic energy and wall shear stress in the early deceleration stage and minima in the late acceleration stage. The wall pressure field is characterized by large fluctuations with respect to the root mean square level, while the skewness and kurtosis of the wall pressure show significant deviations from their Gaussian values. The wall vorticity components show different behaviours during the cycle: for the streamwise component, positive and negative fluctuations have the same probability of occurrence throughout the cycle while the spanwise fluctuations favour negative extrema in the acceleration stage and positive extrema in the deceleration stage. The wall vorticity flux is a function of the wall pressure gradients. Vorticity creation at the wall reaches a maximum at the beginning of the deceleration stage due to the increase of uncorrelated wall pressure signals. The spanwise vorticity component is the most affected by the oscillations of the outer flow. These findings have consequences for the design of wave energy converters. In extreme seas, wave induced fluid velocities can be very high and extreme wall pressure fluctuations may occur. Moreover, the spanwise vortical fields oscillate violently in a wave cycle, inducing strong interactions between vortices and the device that can enhance the device motion.