This paper presents a new technique for realizing continuous 0°-360° RF signal phase shift over a very wide bandwidth. It is based on using single-sideband modulation to-gether with optical filtering to largely suppress one of the RF modulation sidebands over a wide input RF frequency range, and controlling the phase of the optical carrier to shift an RF signal phase. The technique does not require expensive electrical or optical components to realize an RF signal phase shift over 2-40 GHz frequency range with a flat amplitude and phase response performance. This overcomes the current technology limitation in which no reported phase shifter structure has demonstrated the capability of operating in such a wide bandwidth. Experimental results demonstrate only ± 1 dB amplitude variation and ± 5° phase deviation from the desired RF signal phase shift over 2-40 GHz bandwidth and the RF signal amplitude control function. The phase shifter wavelength insensitive performance is also demonstrated experimentally.