The vibrational predissociation spectrum of the argon-tagged ionic cluster (NaCl)32 due to exposure to a chirped infrared laser was theoretically calculated in a time multiscale framework. The response to the laser field is modeled explicitly by molecular dynamics simulations, and statistical rate theories are used to evaluate the long-time dissociation probability. Due to anharmonicities and multiphoton processes, the predissociation spectrum shows some small but systematic red shift in the main absorption line. Negative chirping toward lower frequencies further enhances this effect, and also alters the band intensity and the band width. Positive chirping attenuates the dissociation efficiency.