Algorithmic fairness has attracted significant attention in recent years, with many quantitative measures suggested for characterizing the fairness of different machine learning algorithms. Despite this interest, the robustness of those fairness measures with respect to an intentional adversarial attack has not been properly addressed. Indeed, most adversarial machine learning has focused on the impact of malicious attacks on the accuracy of the system, without any regard to the system's fairness. We propose new types of data poisoning attacks where an adversary intentionally targets the fairness of a system. Specifically, we propose two families of attacks that target fairness measures. In the anchoring attack, we skew the decision boundary by placing poisoned points near specific target points to bias the outcome. In the influence attack on fairness, we aim to maximize the covariance between the sensitive attributes and the decision outcome and affect the fairness of the model. We conduct extensive experiments that indicate the effectiveness of our proposed attacks.