The purpose of the study is the systematization and scientific substantiation of theoretical aspects and practical recommendations for the development of a scientific and methodological approach to evaluating the effectiveness of the circular economy, taking into account the effect of convergence with artificial intelligence, which has been tested on the example of EU countries (2021). The study is devoted to the analytical evaluation and construction of the Ranking Effect of the circular economy with AI. The study was carried out by the method of monitoring the financial support of the implementation of artificial intelligence for the circular economy at EU enterprises, the directions of the use of AI, and at the same time the relationship with the effectiveness, namely the operations of the circular economy, was determined. In a study of the leaders of innovators in the circular economy with AI. In order to outline an effective model of AI implementation in the circular economy, a scientific and methodological approach to evaluation and ranking is proposed. It is emphasized that the convergence of artificial intelligence and the circular economy is primarily aimed at increasing the level of efficiency of resource use and reducing the ecological impact of enterprises on the environment as a whole.