We extend the well-known mapping between the easy-plane ferromagnet and electrostatics in d=2 spatial dimensions to dynamical and quantum phenomena in a d=2+1 spacetime. Ferromagnetic vortices behave like quantum particles with an electric charge equal to the vortex number and a magnetic flux equal to the transverse spin of the vortex core. Vortices with half-integer core spin exhibit fermionic statistics.