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Molecular hydrogen normally has only weak, quadrupole transitions between its rovibrational states, but in a static electric field it acquires a dipole moment and a set of allowed transitions. Here we use published ab initio calculations of the static electrical response tensors of the H2 molecule to construct the perturbed rovibrational eigensystem and its ground state absorptions. We restrict attention to two simple field configurations that are relevant to condensed hydrogen molecules in the interstellar medium: a uniform electric field, and the field of a point-like charge. The energy eigenstates are mixtures of vibrational and angular momentum eigenstates so there are many transitions that satisfy the dipole selection rules. We find that mixing is strongest amongst the states with high vibrational excitation, leading to hundreds of absorption lines across the optical and near infrared. These spectra are very different to that of the field-free molecule, so if they appeared in astronomical data they would be difficult to assign. Furthermore in a condensed environment the excited states likely have short lifetimes to internal conversion, giving the absorption lines a diffuse appearance. We therefore suggest electrified H2 as a possible carrier of the Diffuse Interstellar Bands (DIBs). We further argue that in principle it may be possible to account for all of the DIBs with this one carrier. However, despite electrification the transitions are not very strong and a large column of condensed H2 would be required, making it difficult to reconcile this possibility with our current understanding of the ISM.