Contact is a universal thermodynamic quantity crucial for studying short-range pairing correlations in strongly interacting Fermi gases. It serves as a vital bridge connecting the system's microscopic short-range physics with its macroscopic thermodynamic properties. In this study, we developed a novel two-photon Raman coupling technique for strongly interacting ultracold Fermi gases. This method can switch the interaction to a non-interacting state on timescales much faster than the system's Fermi time, enabling instantaneous measurement of thermodynamic parameters. Our measurements reveal that in the high-momentum region, the atomic gas momentum distribution exhibits a 1/k4 scaling behavior characteristic of Contact, allowing precise determination of the Contact coefficient. Comparison of our experimental results with traditional RF spectroscopy methods and theoretical calculations demonstrates that the two-photon Raman technique achieves accurate Contact measurements comparable to RF methods. Additionally, it offers advantages in transient measurements and immunity to final-state scattering effects. These findings provide crucial experimental evidence for understanding the microscopic mechanisms of strongly correlated Fermi gases.