Polymorph engineering involves the manipulation of material properties through controlled structural modification and is a candidate technique for creating unique two-dimensional transition metal dichalcogenide (TMDC) nanodevices. Despite its promise, polymorph engineering of magnetic TMDC monolayers has not yet been demonstrated. Here we grow FeSe₂ monolayers via molecular beam epitaxy and find that they have great promise for magnetic polymorph engineering. Using scanning tunneling microscopy (STM) and spectroscopy (STS), we find that FeSe₂ monolayers predominantly display a 1T' structural polymorph at 5 K. Application of voltage pulses from an STM tip causes a local, reversible transition from the 1T' phase to the 1T phase. Density functional theory calculations suggest that this single-layer structural phase transition is accompanied by a magnetic transition from an antiferromagnetic to a ferromagnetic configuration. These results open new possibilities for creating functional magnetic devices with TMDC monolayers via polymorph engineering.