We determine the magnetic dipole moment of the rho meson using preliminary data from the BaBar Collaboration for the $e^+ e^- to pi^+ pi^- 2 pi^0$ process, in the center of mass energy range from 0.9 to 2.2 GeV. We describe the $gamma^* to 4pi$ vertex using a vector meson dominance model, including the intermediate resonance contributions relevant at these energies. We find that $mu_rho = 2.1 pm 0.5$ in $e/2 m_rho$ units.