SCORE for Small Business Act of 2023 This bill reauthorizes through FY2025 the Service Corps of Retired Executives (SCORE) program, outlines the duties of the SCORE Association, and requires the Small Business Administration (SBA) to cooperate with the association to carry out the program. Specifically, the bill requires the association to manage nationwide chapters of the program to enable volunteers participating in the program to provide personal, cost-free business expertise and facilitate education workshops to small businesses. The association must also offer online counseling through web-based platforms to small businesses. In consultation with the association, the SBA must ensure that the program (1) recruits diverse volunteers for each chapter of the program, and (2) provides services to rural and underserved communities.