A continuously tunable microwave photonic (MWP) phase shifter based on birefringence effects in a semiconductor optical amplifier (SOA) is presented and the theoretical fundamentals of the design are explained. This proposed device provides a high efficiency phase-shift tuning range beyond 2π rad by controlling the SOA launch power. A prototype of the MWP phase shifter with a frequency of 10 GHz and 2π rad tuning range is experimentally demonstrated.