The dielectric permittivities parallel and perpendicular to thecaxis (optic axis) of ice Ih were measured using an open resonator at 39 GHz in the temperature range 194–262 K. The dielectric anisotropy in ice at microwave frequencies is important for understanding remote sensing data in polar regions, obtained by ice radar and satellite-born microwave radar and radiometer. The measured samples were natural single-crystal ice collected from Mendenhall Glacier, Alaska. A very precise measurement was achieved by detecting two resonant peaks, one from the ordinary component and the other from the extraordinary component, simultaneously, from one sample. The real part of dielectric anisotropy,&Dgr;&egr;′=&egr;∥c′−&egr;⊥c′,at 39 GHz was 0.0339±0.0007 (1.07&percent;±0.02&percent;) at 252 K and slightly depended on temperature. Reference measurements at 1 MHz using parallel plate electrodes were also carried out. The measured dielectric anisotropy at microwave frequencies agrees very well with the value at 1 MHz. The absolute values of&egr;∥c′and&egr;⊥c′at 39 GHz were, respectively, smaller than those at 1 MHz and the difference was about 0.044 at 252 K. The results suggest that a small dispersion exists between GHz and MHz frequencies, but there is no frequency dependence in the value of anisotropy. ©1997 American Institute of Physics.