Fréchet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean responses, our work introduces a novel statistical method for handling random objects with circular predictors. We concentrate on local constant and local linear Fréchet regression, providing rigorous proofs for the upper bounds of both bias and stochastic deviation of the estimators under mild conditions. This research lays the groundwork for broadening the application of Fréchet regression to scenarios involving non-Euclidean covariates, thereby expanding its utility in complex data analysis.