The rotational excitation spectrum, including the vibrational shift of the rotational band, of several CO isotopomers solvated in He clusters has been calculated. Reptation quantum Monte Carlo simulations are used in conjunction with an accurate He-CO potential energy surface, which quantitatively describes the rovibrational spectrum of the binary complex. Our simulations, when compared with number-selective infrared spectra taken for different isotopomers, help discriminate among the alternative assignments proposed for cluster sizes around 15 He atoms. The origin of the vibrational band has a red shift that is nearly linear with the cluster size within the first solvation shell and is almost constant up to the largest cluster studied, well beyond completion of the second solvation shell. A blue upturn at even larger sizes would be needed to attain the nanodroplet limit, as recently estimated from the isotopic dependence of the measured R(0) transitions.