In this paper, we use the temporal quantum correlations in the photon statistics of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the phase space volume occupied by the resonator field, thereby increasing the dependence of its final state on the measured phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until technologies for the generation of highly-entangled many-photon states become more readily available.