Prospect for measurement of CP-violating parameters of $B_s^0\to \phi \gamma$ at the Tera Z factory

$b\to s\gamma$ transition is a critical flavor-changing neutral current (FCNC) process that could be used to probe CP violation (CPV) and new physics (NP). We quantify the anticipated precision for measuring $B_s^0\to \phi \gamma$ at the CEPC Z pole operation, showing that the relative statistical uncertainty could be as low as 0.16%, improved by approximately two orders of magnitude compared to existing measurements. Additionally, we perform a time-dependent analysis of the $B_s^0\to \phi \gamma$ decay, accounting for $B_s^0\mathrm{/}{\bar{B}}_s^0$ mixing extract the mixing-induced and CP-violating parameters $$, $$ and $$. Using central value from LHCb measurement as input, we evaluate the anticipated accuracy of measurements of these parameters. The projected statistical uncertainties are ${\sigma }_{A_{\phi \gamma }^{\mathrm{\Delta }}{}^{\text{stat}}}=0.021$, ${\sigma }_C^{\text{stat}}=0.0092$ and ${\sigma }_S^{\text{stat}}=0.0096$, and the systematic uncertainties are ${\sigma }_{A_{\phi \gamma }^{\mathrm{\Delta }}{}^{\text{syst}}}=0.035$, ${\sigma }_C^{\text{syst}}=0.0027$ and ${\sigma }_S^{\text{syst}}=0.0064$. Furthermore, the 1$\sigma$ sensitivity boundaries for NP in this study are found to be ${\mathcal{A}}_{\phi \gamma }^{\mathrm{\Delta }}<-0.05$ or ${\mathcal{A}}_{\phi \gamma }^{\mathrm{\Delta }}>0.15$, ${\mathcal{C}}_{\phi \gamma }<-0.02$ or ${\mathcal{C}}_{\phi \gamma }>0.04$, and ${\mathcal{S}}_{\phi \gamma }<-0.04$ or ${\mathcal{S}}_{\phi \gamma }>0.04$. We also conduct a relevant detector optimization study by establishing the correlation between the anticipated precision and the intrinsic resolution of the ECAL, as well as the performance of the PID system.