The thriving development of AIGC has catalyzed significant transformations in the design industry, garnering increased scholarly attention to the intersection of these two fields. However, a comprehensive study summarising and revealing the current research status of AIGC in design has yet to be conducted. To address this gap, this study initiated a systematic literature review. Based on the PRISMA framework, journals and conferences were searched for terms related to both AIGC and design, and 90 documents were ultimately included in the corpus for analysis based on strict inclusion and exclusion criteria. This literature review analyzes existing studies' bibliometric data, theoretical foundations, and technological dependencies. Further, it explores the application mechanisms of AIGC in the four stages of the design process: creative divergence, design generation, assistance and advice, evaluation and feedback. By examining the temporal and spatial distribution of existing studies, insights were gained into the evolutionary trends of integrating AIGC with design. This study identifies gaps in the current literature and suggests directions for future research agenda.