We study theoretically the propagation of a guided atom laser across an Aharonov-Bohm ring which is exposed to a synthetic gauge field. The presence of disorder within the ring gives rise to Al'tshuler-Aronov-Spivak oscillations, seen in the disorder average of the transmission as a function of the effective gauge flux that is contained within the ring. Those oscillations are induced by coherent backscattering and represent a manifestation of weak localization. Through analytical and numerical calculations that are based on the mean-field Gross-Pitaevskii approximation for the propagating Bose-Einstein condensate, we show that the presence of a very weak atom-atom interaction within the ring leads to an inversion of the Al'tshuler-Aronov-Spivak oscillations, in a very similar manner as for the coherent backscattering of Bose-Einstein condensates within two-dimensional disorder potentials. Numerical simulations based on the truncated Wigner method reveal that this signature of weak antilocalization becomes washed out if the interaction strength is increased.