A precise determination of the CKM angle γ from \( {B}_s^0 \) oscillations in \( {B}_s^0\to {D}_s^{\mp }{K}^{\pm } \) decays offers a critical test of the Standard Model and probes for new physics. We present a comprehensive study on the prospects of measuring γ at a future Tera-Z factory, utilizing the baseline detector concept of the Circular Electron Positron Collider (CEPC). A two-dimensional simultaneous fit framework, incorporating flavor tagging, decay time resolution modeling, and acceptance corrections, is developed using full Monte Carlo simulations of \( {B}_s^0\to {D}_s^{\mp}\left(\to {K}^{\mp }{K}^{\pm }{\pi}^{\mp}\right){K}^{\pm } \) decays and inclusive background processes. The effective flavor tagging power reaches 23.6%, while the decay time resolution is determined to be 26 fs. Projecting to full statistics of signal events across three dominant \( {D}_s^{-} \) decay channels, we estimate a statistical precision of σ(γ) = 0.69°, which corresponds to 4.1 Tera-Z boson equivalent data. This study has established the feasibility of sub-degree level γ measurements at a Z factory, highlighting its unique advantages in time-dependent CP violation studies through ultra-precise vertexing and background suppression capabilities.
