We have modeled absorption lines of the 12CO and 13CO (∆ υ = 2) molecular bands at λλ 2.29 2.45 µm in the spectrum of Arcturus (K2III). A grid of model atmospheres and synthetic spectra were computed for the red giant using T eff = 4300, log g = 1.5, and the elemental abundances of Peterson et al. (1993), with the exception of the abundances of carbon, log N(C), and oxygen, log N(O) and the carbon isotopic ratio, 12C/13C, which were varied in our computations. The computed spectra were compared to the observed spectrum of Arcturus from the atlas of Hinkle et al. (1976). The best fit between the synthetic and observed spectra is achieved for log N(C) = -3.78, 12C/13C = 8 ± 0.5. We discuss the dependence of 12C/13C on log N(C) and log N(O) in the atmosphere of the red giant.