We propose a method for calculation of the charge distribution along a short (on the wavelength scale) cylindrical antenna in an anisotropic medium and the impedance of the antenna. The method is based on the solution of the corresponding integral equation by using a “thin” antenna approximation for different angles of antenna orientation relative to the anisotropy axes of the medium. The calculation results coincide with the results obtained earlier by other methods if the antenna axis is not too close to the direction of the asymptote of an open wave-vector surface. The case where the antenna is oriented along this asymptote, in the vicinity of which the angular dependence of the real and imaginary parts of the impedance changes abruptly, is considered in detail.