A photonic integrated radio frequency self-interference cancellation chip is designed for full-duplex communication. The radio frequency signals are converted into the optical domain by phase modulation, and the amplitude and phase tuning of the optical carried radio frequency signals is implemented to realize the radio frequency self-interference cancellation function. The optimally designed structural parameters of the cascaded ring are presented. The time delay tuning range is 0 to 10 ps with the delay jitter less than 0.1 ps over 30 GHz bandwidth. For filtering response, the stopband rejection is 36.5 dB, the passband bandwidth is 60.6 GHz, and the steepness of the edge is 9.2 dB/GHz. The theoretical model of the photonic integrated radio frequency self-interference cancellation system is established. The influence of time delay and amplitude mismatch caused by optical delay line, tunable optical attenuator and filter on the radio frequency self-interference cancellation performance is analyzed. With the amplitude mismatch of 0.02 dB, the cancellation depth is -42.7 dB over the bandwidth of 2 GHz. With the time delay deviation of 0.07 ps, the cancellation depth is -37 dB over the bandwidth of 2 GHz. This work paves the way for fabricating the photonic integrated function chip.