  We study theoretically the impact of an applied DC-current on a mesoscopic
chiral $p$-wave superconductor. Performing quasiclassical calculations on a
two-dimensional system, with an external magnetic flux to generate a DC
current, we show that the current can trigger a transition to a state with a
domain wall between regions of different chiralities. The system shows an
hysteretic behavior, as different domain wall configurations are possible for a
given current. This domain wall creation mechanism can give new insights on
recent experiments observing anomalous current variations in Sr${}_2$RuO${}_4$
junctions.
