Reported here is a theoretical calculation of the spectrum of the argon-methane complex based upon a previously reported ab initio potential energy surface [T. G. A. Heijmen et al., J. Chem. Phys. 107, 902 (1997)]. The irregular rotational structure observed in the spectrum is traced to a combination of the fact that the excited vibrational state of the methane has vibrational angular momentum and the methane rotates nearly freely within the complex. The theoretical spectrum is compared qualitatively with the experimental results obtained using the optothermal method, a more complete discussion of which is given in a companion paper, hereafter referred to as paper II.