We investigate the doublet and quartet potential energy surfaces associated with the gas-phase reaction between $Ti^+$ and $CF_3COCH_3$ for two plausible reaction pathways, $TiF_2^+$ and $TiO^+$ formation pathways by using the density functional theory (DFT) method. The molecular structures of intermediates and transition states involved in these reaction pathways are optimized at the DFT level by using the PBE0 functional. All transition states are identified by using the intrinsic reaction coordinate (IRC) method, and the resulting reaction coordinates describe how $Ti^+$ activates $CF_3COCH_3$ and produces $TiF_2^+$ and $TiO^+$ as products. On the basis of presented results, we propose the most favorable reaction pathway in the reaction between $Ti^+$ and $CF_3COCH_3$.