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The measurement of radiation diffraction angles in spectrometers is usually carried out by means of optical encoders or laser interferometers. An angle measurement system based on a ring laser (RL) is described in this paper. The main feature of the RL is that a standing electromagnetic wave in the RL cavity can be considered as a high-precision circular scale. Systems incorporating RLs usually provide an accuracy of angle measurements of several hundredths of an arcsecond in the measurement range 0-. The system described here consists of a RL and an optical interference null-indicator located on a rotary platform optically connected to the crystal of the diffractional spectrometer. An analysis of the measurement principle and measurement errors is presented. It is shown that the main sources of error are the random drift of the phase of the RL output signal and the wideband fluctuation of the null-indicator output signal. Results of measurements of the x-ray line of radiation with an energy of radiation E = 17.47334 keV and corresponding wavelength Å are shown. The angle measurement error of the described system turned out to be about 0.05 arcsecond.