A direct determination of the upper limit for the electric charge density along dislocations in ice has been carried out by measuring the simultaneous effects of an electric field and a mechanical stress on the movement of a low-angle tilt boundary in an ice single crystal. The determination is independent of the geometry of the dislocations or the distribution of the charge along them. No measurable effects of the electric field on boundary motion were found, requiring that the charge density be less than one unit of charge for every 300 atomic lengths of dislocation. This estimate is less than large previous estimates, but is consistent with smaller proposed values.