Understanding the effects of ambient turbulence (expressed often in terms of the turbulence intensity It) is critical to the development of predictive models for the performance of Ocean Current Turbine (OCTs). This paper describes a new, wake interaction modeling framework capable of capturing the detailed effects of turbulence on various performance parameters associated with OCTs that may be arranged in any arbitrary configuration. The model accounts for the effects of turbulence on the structure of the turbine wakes, specifically the extents of near- and far-wake regions, and the dependence of the transition point between the two regions on It. The analytical description for turbine wake is combined with an existing wake interaction model, the Unrestricted Wind Farm Layout Optimization (UWFLO) model to predict the global power output from an array of OCTs. The resulting modelling framework accurately captures the effect of inlet turbulence on the OCT farm power and efficiency, and can be applied to any array configuration. Results from the model are validated against Large Eddy Simulations (LES) in which the OCTs are modeled using the Blade Element Momentum (BEM) model, while the inlet flow is superposed with a synthetic turbulence field designed to approximate turbulence properties obtained from observational measurements of the Gulf Stream. The simulations show that OCT wakes recover faster at higher levels of inlet turbulence due to the enhanced entrainment and mixing between ambient flow and the wake, an effect that is captured by the modified UWFLO model.