We present a spectral theory for the far-infrared absorption spectrum of a very diluted solution of diatomic molecules in a rare-gas fluid, that includes permanent and induced contributions. The absorption coefficient is given as the convolution of a translational spectrum and a rotational spectrum. The former is described in terms of time correlation functions associated to the induced dipole moment. The latter is discussed on the basis of a model consisting of a quantum rigid rotor interacting with a thermal bath, making use of time correlation functions associated to the different anisotropic orders of the solute-solvent intermolecular potential. Non-Markovian and line mixing effects are taken into account. Explicit expressions for the five leading contributions of the induced dipole moment are given.