In physical therapy, exercises improve range of motion, muscle strength, and flexibility, where motion-tracking devices record motion data during exercises to improve treatment outcomes. Cameras and inertial measurement units (IMUs) are the basis of these devices. However, issues such as occlusion, privacy, and illumination can restrict vision-based systems. In these circumstances, IMUs may be employed to focus on a patient’s progress quantitatively during their rehabilitation. In this study, a 3D rigid body that can substitute a human arm was developed, and a two-stage algorithm was designed, implemented, and validated to estimate the elbow joint angle of that rigid body using three IMUs and incorporating the Madgwick filter to fuse multiple sensor data. Two electro-goniometers (EGs) were linked to the rigid body to verify the accuracy of the joint angle measuring algorithm. Additionally, the algorithm’s stability was confirmed even in the presence of external acceleration. Multiple trials using the proposed algorithm estimated the elbow joint angle of the rigid body with a maximum RMSE of 0.46°. Using the IMU manufacturer’s (WitMotion) algorithm (Kalman filter), the maximum RMSE was 1.97°. For the fourth trial, joint angles were also calculated with external acceleration, and the RMSE was 0.996°. In all cases, the joint angles were within therapeutic limits.