Specialty Crop Domestic Market Promotion and Development Program Act of 2023 This bill directs the Agricultural Marketing Service to establish a grant program to encourage the development, maintenance, and expansion of the commercial domestic market for domestically produced specialty crop commodities (e.g., for advertising or other demand-oriented, generic domestic promotion activities). Organizations eligible for the grant program include those that promote U.S. produced and grown specialty crop sales and are (1) U.S. agricultural trade organizations or regional state-related organizations that do not profit directly from U.S. specialty crop sales, (2) cooperative organizations or state agencies, or (3) certain private organizations. Specialty crop organizations operating under federal marketing orders are also eligible for the grant program.