In this paper, an effective synthesis method for sparse uniformly excited concentric ring array (CRA) element positions featuring a minimum sidelobe level (SLL) is presented. This method is based on the chaos sparrow search algorithm (CSSA), which can search for the optimal solution under multiple constraints. By improving the constraint on the number of array elements on each ring, the solution range of the optimal solution is further reduced, and the global search ability of the algorithm is effectively improved by introducing tent mapping into the algorithm to initialize the population. Numerical examples are presented to assess the effectiveness and reliability of the proposed method, showing that it can achieve better results than existing methods in the design of sparse concentric ring array arrangements.