Growing evidence suggests that social determinants of health (SDoH), a set of nonmedical factors, affect individuals' risks of developing Alzheimer's disease (AD) and related dementias. Nevertheless, the etiological mechanisms underlying such relationships remain largely unclear, mainly due to difficulties in collecting relevant information. This study presents a novel, automated framework that leverages recent advancements of large language model (LLM) and natural language processing techniques to mine SDoH knowledge from extensive literature and integrate it with AD-related biological entities extracted from the general-purpose knowledge graph PrimeKG. Utilizing graph neural networks, we performed link prediction tasks to evaluate the resultant SDoH-augmented knowledge graph. Our framework shows promise for enhancing knowledge discovery in AD and can be generalized to other SDoH-related research areas, offering a new tool for exploring the impact of social determinants on health outcomes. Our code is available at: https://github.com/hwq0726/SDoHenPKG