Charge Transfer (CT) has enjoyed continuous interest due to increasing experimental control over molecular structures, leading to applications in, for example, photovoltaics and hydrogen production. In this paper, we investigate the effect of CT states on the absorption spectrum of linear molecular aggregates using a scattering matrix technique that allows us to deal with arbitrarily large systems. The presented theory performs well for both strong and weak mixing of exciton and CT states, bridging the gap between previously employed methods, which are applicable in only one of these limits. In experimental spectra, the homogeneous linewidth is often too large to resolve all optically allowed transitions individually, resulting in a characteristic two-peak absorption spectrum in both the weak- and strong-coupling regime. Using the scattering matrix technique, we examine the contributions of free and bound states in detail. We conclude that the skewness of the high-frequency peak may be used as a new way to identify the exciton-CT-state coupling strength.