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.