A time-domain atom interferometer with a cold calcium atomic ensemble has been developed with a phase resolution ${\ensuremath{\sigma}}_{\ensuremath{\varphi}}=140/\sqrt{\ensuremath{\tau}}$ mrad/s${}^{1/2}$ at the integration time $\ensuremath{\tau}$. Using this atom interferometer, the dispersion-shaped ac Stark phase shift with a sharp reversal on resonance was demonstrated under the perturbation light near the resonance frequency of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0},\phantom{\rule{4pt}{0ex}}{m}_{J}=0{\ensuremath{-}}^{3}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}{P}_{1},\phantom{\rule{4pt}{0ex}}{m}_{J}=\ensuremath{-}1$ transition. The phase shift was well described by a convolution of functions of the ac Stark potential and a Rabi excitation, and it was found that the lifetime of the ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.