We propose a distributionally robust support vector machine with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive an exact reformulation for worst-case unfairness measure. We establish that the model is equivalent to a mixed-binary optimization problem, which can be solved by standard off-the-shelf solvers. We further prove that the expectation of the hinge loss objective function constitutes an upper bound on the misclassification probability. Finally, we numerically demonstrate that our proposed approach improves fairness with negligible loss of predictive accuracy.