A high-finesse Fabry–Perot cavity with a frequency-doubled continuous wave green laser (532nm) has been built and installed in Hall A of Jefferson Lab for high precision Compton polarimetry. The infrared (1064nm) beam from a ytterbium-doped fiber amplifier seeded by a Nd:YAG nonplanar ring oscillator laser is frequency doubled in a single-pass periodically poled MgO:LiNbO3 crystal. The maximum achieved green power at 5W infrared pump power is 1.74W with a total conversion efficiency of 34.8%. The green beam is injected into the optical resonant cavity and enhanced up to 3.7kW with a corresponding enhancement of 3800. The polarization transfer function has been measured in order to determine the intra-cavity circular laser polarization within a measurement uncertainty of 0.7%. The PREx experiment at Jefferson Lab used this system for the first time and achieved 1.0% precision in polarization measurements of an electron beam with energy and current of 1.06GeV and 50μA.