Scoring the driving performance of various drivers on a unified scale, based on how safe or economical they drive on their daily trips, is essential for the driver profile task. Connected vehicles provide the opportunity to collect real-world driving data, which is advantageous for constructing scoring models. However, the lack of pre-labeled scores impede the use of supervised regression models and the data privacy issues hinder the way of traditionally data-centralized learning on the cloud side for model training. To address them, an unsupervised scoring method is presented without the need for labels while still preserving fairness and objectiveness compared to subjective scoring strategies. Subsequently, a federated learning framework based on vehicle-cloud collaboration is proposed as a privacy-friendly alternative to centralized learning. This framework includes a consistently federated version of the scoring method to reduce the performance degradation of the global scoring model caused by the statistical heterogeneous challenge of local data. Theoretical and experimental analysis demonstrate that our federated scoring model is consistent with the utility of the centrally learned counterpart and is effective in evaluating driving performance.