Routing, core selection and spectrum assignment in multi-core elastic optical networks are studied. A global constrained optimization model is established, and a heuristic algorithm and its improved algorithm based on core rotation selection are proposed. In the improved alginthm, connection requests are classified according to different sorting strategies. Connection requests are classified into different groups according to source node, destination node and the selected routing, the selection mechanism based on core rotation in the same connection request group is employed, and the first-fit method is used in spectrum assignment for the selected core. Simulations are conducted in two networks, and the results indicate that the proposed algorithm and its improved algorithm can obtain better scheme of routing and core selection than the compared algorithms.