We explore a new mechanism for switching magnetism and superconductivity in a magnetically frustrated iron-based superconductor using spin-polarized scanning tunneling microscopy (SPSTM). Our SPSTM study on single-crystal Sr2VO3FeAs shows that a spin-polarized tunneling current can switch the Fe-layer magnetism into a nontrivial C4 (2×2) order, which cannot be achieved by thermal excitation with an unpolarized current. Our tunneling spectroscopy study shows that the induced C4 (2×2) order has characteristics of plaquette antiferromagnetic order in the Fe layer and strongly suppresses superconductivity. Also, thermal agitation beyond the bulk Fe spin ordering temperature erases the C4 state. These results suggest a new possibility of switching local superconductivity by changing the symmetry of magnetic order with spin-polarized and unpolarized tunneling currents in iron-based superconductors.