Flexible sensor technology has a great significance in fields, such as human joint motion signal detection. We proposed a flexible detachable capacitive sensor based on nonparallel electrodes fixed on the inner side of the finger joint. The sensing unit was composed of copper electrode, barium titanate (BaTiO3)/polydimethylsiloxane (PDMS) film, and polyimide (PI) tape. The relative area and distance of the electrodes and the relative dielectric constant of the dielectric layer were changed with the rotation of the finger joint. A theoretical model of the sensor was established, and the function relationship between capacitance and finger joint bending angle was reflected. The sensor improved the previous problems of hysteresis and lack of stability caused by uneven force, unsecure install, and material viscoelasticity when the sensor was directly attached to the measured finger joint. The results indicate that the sensor has potential application value in fields, such as sports rehabilitation and joint disease assessment.