Aided inertial navigation system (INS), typically consisting of an inertial measurement unit (IMU) and an exteroceptive sensor, has been widely accepted as a feasible solution for navigation. Compared with vision-aided and LiDAR-aided INS, radar-aided INS could achieve better performance in adverse weather conditions since the radar utilizes low-frequency measuring signals with less attenuation effect in atmospheric gases and rain. For such a radar-aided INS, accurate spatiotemporal transformation is a fundamental prerequisite to achieving optimal information fusion. In this work, we present RIs-Calib: a spatiotemporal calibrator for multiple 3D radars and IMUs based on continuous-time estimation, which enables accurate spatiotemporal calibration and does not require any additional artificial infrastructure or prior knowledge. Our approach starts with a rigorous and robust procedure for state initialization, followed by batch optimizations, where all parameters can be refined to global optimal states steadily. We validate and evaluate RIs-Calib on both simulated and real-world experiments, and the results demonstrate that RIs-Calib is capable of accurate and consistent calibration. We open-source our implementations at (https://github.com/Unsigned-Long/RIs-Calib) to benefit the research community.