Accurate and reliable sensor extrinsic calibration methods are crucial for high-precision localization and navigation in radar-inertial fusion systems. However, most existing calibration methods rely on the acquisition of triaxial excitation from inertial sensors, and their performance deteriorates or even fails when the radar and inertial sensors are installed on ground robots with restricted movement. To address this issue, a novel calibration method based on planar features in radar point clouds is proposed for radar-inertial odometry on ground robots. The method first constructs residuals using planar features in the radar point clouds and rapidly converges the extrinsic parameters to a smaller error range by minimizing the distance from radar points to the planes. Subsequently, it further optimizes the extrinsic parameters based on the octree structure, incorporating the spatial occupancy information of the radar point clouds. Finally, by integrating ground constraints through a ground segmentation algorithm, the method corrects the errors in the Z-axis direction that cannot be constrained during planar motion, thereby achieving complete 6-DOF (degrees of freedom) extrinsic parameters. Experimental results show that the proposed method significantly outperforms other algorithms in calibration accuracy on two open-source datasets, with average rotational angle errors reduced by 43.73% and 36.47%, and average translational errors reduced by 76.33% and 41.52%, respectively. In real-world vehicle validation experiments, the method successfully achieves calibration in various scenarios, including flat terrain, rugged terrain, and narrow passages, further demonstrating its reliability and robustness in practical environments. In localization accuracy analysis experiments, the absolute trajectory root mean square error of the FAST-LIO2 algorithm, initialized with the calibration results of this paper, is reduced by approximately 6.54%, evaluating the practicality and accuracy of the proposed method.