We report on the observation of spontaneous coherent oscillations in a microcavity polariton bosonic Josephson junction. Condensation of exciton polaritons here takes place under incoherent excitation in a double potential well naturally formed in the disorder. Coherent oscillations set on at an excitation power well above the condensation threshold. The time resolved population and phase dynamics reveal the analogy with the ac Josephson effect. A theoretical two-mode model describes the observed effects, explaining how the different realizations of the pulsed experiment can be in phase.