This study investigates the effect of turbulence intensity on wind turbine induction factor and power efficiency through its influence on the turbine wake. Two different scenarios are systematically analyzed: (1) a stand-alone wind turbine sited on flat terrain with different aerodynamic roughness and (2) a wind turbine in the wake of another turbine with varying turbine spacing. Overall, the incoming turbulence intensity ranges from 4.6% to 22.3%, covering a wide range of turbulence intensity. The results indicate that increasing incoming turbulence intensity consistently reduces the turbine wake deficit, particularly near the turbine, while the turbine induction factor decreases and the power coefficient increases. This means that turbines operating in higher incoming turbulence produce more power for an equivalent wind potential, with a maximum efficiency difference of about 10% across all cases. The study identifies clear relationships between the turbine power coefficient, induction factor, maximum wake deficit, and incoming turbulence intensity. The findings demonstrate a strong connection between the turbine power efficiency and the wake development. This effect is in addition to the well-known influence of turbulence intensity on the turbine power due to the nonlinear relationship between the turbine power and the incoming wind speed. In this context, the results demonstrate a clear linear relationship between the power coefficient and the incoming turbulence intensity. Ultimately, this relationship could serve as a predictive tool for assessing the effect of turbulence intensity on power efficiency.