THE strengths of ultraviolet absorption lines of interstellar hydrogen have been measured in the spectra of several reddened early-type stars1-3. Interstellar H2 molecules are observed mainly in the two lowest rotational levels J = 0 (para-H2) and J = 1 (ortho-H2) with a ratio of populations corresponding to an average temperature ~ 80 K. This temperature is consistent with the mean HI kinetic temperature determined in 21-cm absorption studies4,5, whereas higher rotational levels up to J = 5 or 6 are populated corresponding to significantly higher excitation temperatures3,6 in the range 150-200K. These observations indicate that a process other than thermal gas collisions is responsible for populating the higher rotational levels. The precise nature of the excitation mechanism is as yet unknown. A process which could contribute to non-thermal excitation of rotational levels involves encounters of charged dust grains with interstellar hydrogen. We have examined this mechanism and find that it could be of comparable, if not greater, importance in relation to other processes which have been proposed.