While all of the polymorphs of NH4I and NH4Br are nonpolar, a reversible electric polarization is established in the ordered γ phases of (NH4)0.73(ND4)0.27I and (NH4)0.84(ND4)0.16Br (where D is 2H) via dc electric fields. The presence of two groups of orbital magnetic moments appears to be responsible for the asymmetric lattice distortions. Our findings provide an alternative pathway for hydrogen-based materials to potentially add a ferroelectric functionality.