An all-optical 4-way photonic RF power splitter with quadrature-phase outputs is presented. It is based on using the new power splitting and independent optical phase control function in a Fourier-domain optical processor to split a single-wavelength phase modulated optical signal into four with the desired optical phases at different frequencies and route them to four different output ports. It solves the large phase error problem in the electrical quadrature-phase power dividers, and has the advantages of infinite isolation and a reconfigurable RF power splitting ratio. Experimental results are presented that demonstrate a 4-way photonic RF hybrid splitter with a 3-dB operating frequency range from 10.5 GHz to 26.5 GHz, an amplitude imbalance of less than 1 dB and a phase error of less than ±0.35°. The reconfigurable RF power splitting ratio of the hybrid splitter is also demonstrated experimentally.