Lower lying rovibrational energy levels of the acetylene-Cl-anion complex are calculated using an ab initio potential energy surface (PES) computed at MP2/aug-cc-pVTZ level. The PES is characterized by a deep minimum in the linear configuration (D-e=3760 cm-1, R-e=3.97 A) and a purely repulsive interaction for a T-shaped configuration. Rovibrational calculations are performed on PESs that are adiabatically corrected for the influence of the local mode vibration of the intermediate proton (hydrogen-bonded C-H stretch mode). The adiabatic correction leads to an enhanced intermolecular interaction with a deepening of the potential well and shortening of the equilibrium intermolecular separation. These effects becomes more pronounced as additional quanta are added to the hydrogen-bonded nu(CH) stretch mode. Band energies and rotational constants are calculated for states likely to be observable in spectroscopic searches. The predicted complexation-induced frequency shift for the acetylene nu(3) vibration is -446 cm(-1).