Quantum-entangled photons have drawn considerable attention for application in quantum cryptography and quantum computers. The optical systems used for measuring polarization-entangled states mostly consist of free-space optical components, which are bulky and sensitive to environmental changes and requires persistent optical alignment. In this study, we propose a solution for the stable measurement of the quantum entanglement of photons based on polymeric waveguide integrated optics. The proposed system consists of two quarter-wave plates inserted in a polymeric optical waveguide, an asymmetric X-junction optical waveguide, four birefringence modulators, and two polarizing beam splitters. The basic performance of the integrated optic device has been confirmed using a 1550-nm distributed feedback laser. High polarization conversion and splitting efficiencies are demonstrated, which are important for the measurement of entangled photon states.