The potential use of high sensitivity laser absorption spectroscopy for measuring the 13C/12C isotope ratio in atmospheric CO2 has been demonstrated, using a GaSb-based diode laser at 2.05 microm. In this spectral region, the overlapping between relatively strong 12CO2 and 13CO2 absorption features gives rise to several line pairs which are well suitable for a spectroscopic determination of the isotope ratio. Preliminary results have demonstrated that a short-term precision better than 1 per thousand can be easily obtained, for a CO2 concentration of 1000 ppm. We extensively discuss the influence of a possible non-linearity in the detectors' response on the delta-value and suggest an instrumental development that would allow to eliminate this effect.