With the introduction of new generation high speed routers, and with the help of "flow-aware" traffic management, it becomes possible to improve the Quality of Service for users as well as the network efficiency for ISPs. An example of the "flow-aware" traffic management is the Alcatel-Lucent "Semantic Networking" framework where short-lived flows are processed with high priority and long-lived flows are controlled on a per flow basis. In order to control efficiently the flows, it is useful to know an estimate of the Round Trip Time (RTT). In the present work, we provide an online RTT estimation algorithm which is passive and needs one-way traffic only. The one-way traffic requirement is essential for the application of the algorithm for "flow-aware" traffic management inside the network. To the best of our knowledge, there was no online one-way traffic RTT estimators. Tests on a controlled testbed and on the Internet demonstrate high accuracy of the proposed estimator.