The growth of digital communications has driven the development of numerous cryptographic methods for secure data transfer and storage. The SHA-256 algorithm is a cryptographic hash function widely used for validating data authenticity, identity, and integrity. The inherent SHA-256 computational overhead has motivated the search for more efficient hardware solutions, such as application-specific integrated circuits (ASICs). This work presents a custom ASIC hardware accelerator for the SHA-256 algorithm entirely created using open-source electronic design automation tools. The integrated circuit was synthesized using SkyWater SKY130 130 nm process technology through the OpenLANE automated workflow. The proposed final design is compatible with 32-bit microcontrollers, has a total area of 104,585 µm2, and operates at a maximum clock frequency of 97.9 MHz. Several optimization configurations were tested and analyzed during the synthesis phase to enhance the performance of the final design.