We study the phase shift induced by atomic interactions at the output of an atom interferometer. Due to the mutual interaction between the two overlapping Bose-Einstein condensates, the phase exhibits a spatial profile. We evaluate the phase gradient using a perturbative method based on the Feynman path-integral approach. Our model accounts for the effects of the population imbalance between the two arms of the interferometer and the difference between the scattering lengths of the hyperfine levels. We also investigate these effects experimentally by measuring the interaction phase shift for a set parameters. Our experimental results are well reproduced by our theoretical model.