The Jiangmen Underground Neutrino Observatory (JUNO) Central Detector (CD) is a huge acrylic spherical vessel containing 20,000 tons of liquid scintillator; the sphere is composed of 263 pieces of acrylic spherical panels bonded by the mass polymerization. The operation life time of the JUNO CD is 20 years. To ensure the structural safety during the JUNO CD life time, the acrylic stress of CD is required not to be greater than 3.5 MPa. The stresses of acrylic spherical panels are required to be measured during the installation on-site; unfortunately there is no suitable commercial measurement equipment that can meet JUNO's requirements. Therefore, a measurement setup based on photo-elastic principle and spectrometric methods was designed, developed and tested for on-site measurements. The measurement system performs accurate calibration of stress-optical coefficient of acrylic in JUNO, and gives reliable results of acrylic stresses. The measurement system has been tested in the Taixing Donchamp Acrylic Ltd mechanical workshop, and the achieved results meet the JUNO's requirements. The measurement principle, the system components, and the tooling design are introduced in the paper. Moreover, the calibration of stress-optical coefficient of the acrylic and measurements results on JUNO acrylic spherical panels are discussed in the following.