Recent years have witnessed the pivotal role of Graph Neural Networks (GNNs) in various high-stake decision-making scenarios due to their superior learning capability. Close on the heels of the successful adoption of GNNs in different application domains has been the increasing societal concern that conventional GNNs often do not have fairness considerations. Although some research progress has been made to improve the fairness of GNNs, these works mainly focus on the notion of group fairness regarding different subgroups defined by a protected attribute such as gender, age, and race. Beyond that, it is also essential to study the GNN fairness at a much finer granularity (i.e., at the node level) to ensure that GNNs render similar prediction results for similar individuals to achieve the notion of individual fairness. Toward this goal, in this paper, we make an initial investigation to enhance the individual fairness of GNNs and propose a novel ranking based framework---REDRESS. Specifically, we refine the notion of individual fairness from a ranking perspective, and formulate the ranking based individual fairness promotion problem. This naturally addresses the issue of Lipschitz constant specification and distance calibration resulted from the Lipschitz condition in the conventional individual fairness definition. Our proposed framework REDRESS encapsulates the GNN model utility maximization and the ranking-based individual fairness promotion in a joint framework to enable end-to-end training. It is noteworthy mentioning that REDRESS is a plug-and-play framework and can be easily generalized to any prevalent GNN architectures. Extensive experiments on multiple real-world graphs demonstrate the superiority of REDRESS in achieving a good balance between model utility maximization and individual fairness promotion. Our open source code can be found here: https://github.com/yushundong/REDRESS.