To search for new evidence of the chiral p-wave superconducting domain in Sr2RuO4, we investigated the unconventional local transport characteristics of a microfabricated Sr2RuO4-Ru eutectic junction. We found that the anomalous hysteresis in voltage-current characteristics [as reported in H. Kambara et al.: Phys. Rev. Lett. 101 (2008) 267003.] is strongly affected by dc currents, but not by magnetic fields. This suggests that dc current acts as a driving force to move chiral p-wave domain walls; a domain wall trapped at a pinning potential is forced to shift to the next stable position, thereby forming a larger critical current path and resulting in the anomalous hysteresis.