Reliable and accurate calibration for camera, inertial measurement unit (IMU) and robot is a critical prerequisite for visual-inertial based robot pose estimation and surrounding environment perception. However, traditional calibrations suffer inaccuracy and inconsistency. To address these problems, this paper proposes a monocular visual-inertial and robotic-arm calibration in a unifying framework. In our method, the spatial relationship is geometrically correlated between the sensing units and robotic arm. The decoupled estimations on rotation and translation could reduce the coupled errors during the optimization. Additionally, the robotic calibration moving trajectory has been designed in a spiral pattern that enables full excitations on 6 DOF motions repeatably and consistently. The calibration has been evaluated on our developed platform. In the experiments, the calibration achieves the accuracy with rotation and translation RMSEs less than 0.7° and 0.01 m, respectively. The comparisons with state-of-the-art results prove our calibration consistency, accuracy and effectiveness.