A compact and portable diode-laser spectrometer is developed for high-precision measurements of the 13CO2/12CO2 isotope ratio. Ro-vibrational transitions belonging to different combination bands, around 2.008 µm, are detected for the two isotopomers, using wavelength-modulation spectroscopy with first-harmonic detection. The determination of the isotope ratio is performed through a comparison between the spectra, simultaneously acquired in two different multiple-reflection cells designed to contain the sample and reference gases. The reproducibility of our method is extensively investigated over different time scales. In particular, the short-term precision of the isotope ratio determination is found to be 0.03%. We discuss the presence of possible systematic shifts in the δ-value and optimise the operating conditions to ensure accuracy within the precision level. A possible use for in-situ measurements in volcanic gases is also discussed.