This study investigates the intrinsic electric dipole moment (EDM) of the $\textit{τ}$ lepton, which is an important quantity in the search for physics beyond the Standard Model (BSM). In preparation for future measurements at the Super Tau-Charm Facility (STCF), we employ Monte Carlo simulations of the $ e^+e^- \rightarrow \tau^+\tau^- $ process and optimize the analysis methodology for EDM extraction. Machine learning techniques are implemented to efficiently identify signal events ( $ \tau^\pm\rightarrow \pi^\pm\pi^0\nu_\tau $ ), which result in a significant improvement in signal-to-noise ratio. Our optimized event selection algorithm achieves 80.0% signal purity with 6.3% efficiency. We develop an analytical approach for $\textit{τ}$ lepton momentum reconstruction and derive the squared spin density matrix along with optimal observables, which maximize the sensitivity to $ d_\tau $ . The relationship between these observables and the EDM is established with the estimated sensitivity of $ |d_\tau| \lt 3.89\times 10^{-18}\,e\cdot\mathrm{cm} $ at a 68% confidence level. These results provide a foundation for future experimental measurements of the $\textit{τ}$ lepton EDM in STCF experiments.