The rising influence of artificial intelligence (AI) enables widespread adoption of the technology in every aspect of computing, including Software-Defined Networking (SDN). Technological adoption leads to the convergence of AI and SDN, producing solutions that overcome limitations present in traditional networking architecture. Although numerous review articles discuss the convergence of these technologies, there is a lack of bibliometric trace in this field, which is important for identifying trends, new niches, and future directions. Therefore, this study aims to fill the gap by presenting a thorough bibliometric analysis of AI-related SDN studies, referred to as AI-SDN. The study begins by identifying 474 unique documents in the Web of Science (WoS) database published from 2009 until recently. The study uses bibliometric analysis to identify the general information, countries, authorship, and content of the selected articles, thereby providing insights into the geographical and institutional landscape shaping AI-SDN research. The findings provide a robust roadmap for further investigation in this field, including the background and taxonomy of the AI-SDN field. Finally, the article discusses several challenges and the future of AI-SDN in academic research.