A novel normal measurement device for robotic drilling and countersinking has been developed in this paper. This device is mainly composed of three contact displacement sensors and a spherically compliant clamp pad. The compliance of the clamp pad allows it to be perpendicular to the part when the Multi-Function End Effector (MFEE) drives it to clamp the part surface prior to drilling, while the displacement sensors are used to measure the movement of the clamp pad relative to the MFEE. Once the sensors’ position is calibrated, the rotation angle of the clamp pad can be calculated by the displacement of the sensors. Then, the normal adjustment of MFEE is obtained, and the adjustment process can be achieved by the Tool Center Point (TCP) function of robot. Thus, an innovative method based on laser tracker to identify the position of sensors is proposed. The datum plane for calibration can be measured by the laser tracker, and the least square plane fitting method is used to improve the precision. Meanwhile, the function about the sensors’ position can be established by measuring the calibrated datum using the normal measurement device. As there are two unknown parameters for each sensor’s position, thus the sensors can be calibrated by two unparallel datum planes. Through the experimental verification, the specially designed normal measurement device with the proposed calibration method is able to perform the high-accuracy drilling and countersinking on parts with robotic drilling system.