We study a covert queueing channel (CQC) between two users sharing a round robin scheduler. Such a covert channel can arise when users share a resource such as a computer processor or a router arbitrated by a round robin policy. We present an information-theoretic framework to model and derive the maximum reliable data transmission rate, i.e., the capacity of this channel, for both noiseless and noisy setups. Our results show that seemingly isolated users can communicate with a high rate over the covert channel and demonstrate the possibility of significant information leakage and privacy threats brought by CQCs in round robin schedulers. Moreover, we propose practical finite-length code constructions, which achieve the capacity limit.