In this paper, we present a framework for predicting the personality traits by analyzing tweets written in Turkish. The prediction model is constructed with a clustering based approach. Since the model is based on linguistic features, it is language specific. The prediction model uses features applicable to Turkish language and related to writing style of Turkish Twitter users. Our approach uses anonymous BIGS questionnaire scores of volunteer participants as the ground truth in order to generate personality model from Twitter posts. Experiment results show that constructed model can predict personality traits of Turkish Twitter users with relatively small errors.