We present a search strategy for neutrino-induced air showers using the Telescope Array surface detectors (TA SD), with a focus on the large zenith angle region. To develop this analysis method, we employed dedicated Monte Carlo (MC) simulations. While previous TA analyses primarily used MC generation techniques for proton showers with zenith angles up to 60 degrees, we have extended and validated a new MC generation approach tailored to large-zenith-angle neutrino showers. Furthermore, we developed an optimized reconstruction method designed specifically for neutrino-induced inclined air showers. Using the generated MC datasets, we establish a strategy to discriminate neutrino showers from proton showers effectively. In this talk, we introduce this new neutrino search framework for the TA experiment. The developed methodology is ready to be applied to the real data collected by the TA SD to pursue a search for neutrino candidates.