The current density evolution in YBa2Cu3O7−δ thin films is studied by time-resolved magneto-optical imaging as a function of the phase of an ac current applied simultaneously with a perpendicular dc magnetic field. We present a new empirical method to separate the total current distribution into a circulating current, which screens the applied field, and the applied transport current. The latter shows an asymmetric profile with pronounced peaks at the edges of the sample and its phase-dependent self-field is contained in the flux region bound by the circulating current. Threading dislocations provide the necessary pinning sites for the observed high local values of the transport current.