Accurate time synchronization between heterogeneous sensors is crucial for ensuring robust state estimation in multi-sensor fusion systems. Sensor delays often cause discrepancies between the actual time when the event was captured and the time of sensor measurement, leading to temporal misalignment (time offset) between sensor measurement streams. In this paper, we propose an extended Kalman filter (EKF)-based radar-inertial odometry (RIO) framework that estimates the time offset online. The radar ego-velocity measurement model, derived from a single radar scan, is formulated to incorporate the time offset into the update. By leveraging temporal calibration, the proposed RIO enables accurate propagation and measurement updates based on a common time stream. Experiments on both simulated and real-world datasets demonstrate the accurate time offset estimation of the proposed method and its impact on RIO performance, validating the importance of sensor time synchronization. Our implementation of the EKF-RIO with online temporal calibration is available at https://github.com/spearwin/EKF-RIO-TC.