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We propose and experimentally demonstrate a tunable silicon photonic radio frequency (RF) phase shifter with low power variation based on constructive interference of an add-drop ring resonator. The thermal nonlinear effect of the add-drop ring resonator is used to realize a nearly 2π-phase shift, and the RF power variation is minimized by allowing two lights at the outputs of the add-drop ring resonator to combine at a directional coupler to achieve constructive interference. By thermally tuning the add-drop ring resonator, a nearly 2π-phase shift is realized and the operation is verified by an experiment. Experimental results show that a 0-5.2-rad phase-shift range with an RF power variation within 0.2 dB for a frequency range of a 40-GHz signal is achieved by thermally tuning the ring resonator. A phase shift up to 4.1 rad over a frequency range of 20-40 GHz is also realized.