Monitoring of the 13CO2/12CO2 ratio in the atmosphere is one of the most important tasks of carbon cycle and global climate change control. The method of remote sensing of the column-averaged 13CO2/12CO2 ratio in the atmosphere is proposed for the first time. It is based on measuring the ratio of atmospheric optical depths for a homologous couple of 13CO2 and 12CO2 lines in high resolution transmittance spectra of solar radiation within range 6100-6300 cm-1, which depends only on the columnar ratio 13CO2/12CO2 and does not depend on variations of temperature profile and solar zenith angle. A possibility of application of the method to atmospheric transmittance spectra measured with modern FTIR in the cloudless aerosol-free atmosphere is discussed.