The optimisation of the Area Under the ROC Curve (AUC) has recently been proposed for learning ranking functions. However, the estimation of the AUC of a function on the true distribution of the examples based on its empirical value is still an open problem. In this paper, we present a data-dependent generalisation error bound for the AUC. This bound presents the advantage to be tight, but it also allows to draw practical conclusions on learning algorithms which optimise the AUC. In particular, we show that in the case of AUC, kernel function classes have strong generalisation guarantees provided that the weights of the functions are small, suggesting that regularisation procedures which tend to limit the norm of the weight vector may lead to better generalisation performance for algorithms which optimise the AUC.