Reconfigurable antenna multiple-input multiple-output (MIMO) is a promising technology for upcoming 6G communication systems. In this paper, we deal with the problem of configuration selection for reconfigurable antenna MIMO by leveraging Coherent Ising Machines (CIMs). By adopting the CIM as a heuristic solver for the Ising problem, the optimal antenna configuration that maximizes the received signal-to-noise ratio is investigated. A mathematical framework that converts the selection problem into a CIM-compatible unconstrained quadratic formulation is presented. Numerical studies show that the proposed CIM-based design outperforms classical counterparts and achieves near-optimal performance (similar to exponentially complex exhaustive searching) while ensuring polynomial complexity.