In this paper the statistics of the wall shear stress in acceleration-skewed oscillatory flows are studied by means of direct numerical simulations. The topic is of interest because of its implications in the understanding of various phenomena that take place at the bottom of sea waves. The results show that the spatial distribution of the wall shear stress is strongly inhomogeneous during the accelerating phase and in particular when the phase averaged wall shear stress grows rapidly. Negative values of the fluctuating wall shear stress component are more frequent than positive ones, but the largest values are positive. The relative intensity, given by the ratio between the root mean square of the wall shear stress fluctuations and the phase averaged value, rapidly increases during the first stage of the accelerating phase up to values of about 0.4-0.45. Then these values are maintained for a significant time interval that is longer when the Reynolds number increases. The skewness of the probability density of the wall shear stress fluctuations is positive during the first half cycle and negative during the second one. The skewness is large when the turbulence is well developed while it becomes small when the flow tends to laminarize.