Clustering and analyzing on collected data can improve user experiences and quality of services in big data, IoT applications. However, directly releasing original data brings potential privacy concerns, which raises challenges and opportunities for privacy-preserving clustering. In this paper, we study the problem of non-interactive clustering in distributed setting under the framework of local differential privacy. We first extend the Bit Vector, a novel anonymization mechanism to be functionality-capable and privacy-preserving. Based on the modified encoding mechanism, we propose kCluster algorithm that can be used for clustering in the anonymized space. We show the modified encoding mechanism can be easily implemented in existing clustering algorithms that only rely on distance information, such as DBSCAN. Theoretical analysis and experimental results validate the effectiveness of the proposed schemes.