The supply level of irrigation and water conservancy is related to the utilization efficiency of water resources, the production level of farmers, and the supply quality of agricultural products, especially relating to national food security and stability. Based on 1169 pieces of data collected from field surveys in three provinces of China in 2019, an evaluation system of social network relationships was constructed from five aspects: network scale, network tightness, trust and commitment, social atmosphere and sense of belonging, and social participation. These five aspects are the channels for farmers to obtain information. A binary logistic model was used to analyze the impact of the social network relationships on farmers’ participation in small water-saving irrigation and water conservancy facilities supply, and the key factors affecting farmers’ behavior were selected. The purpose of this study is to further improve the evaluation system of social network relationships and the study of the effect of social network relationships on farmers’ water-saving behaviors, enrich relevant theories and provide a feasible path for the implementation of water-saving irrigation from the macro initiative level. The results show that higher network closeness and policy satisfaction, water management experience, agricultural insurance, strong family decision-making power, etc., will reduce the likelihood of farmers participating in the supply of small water-saving irrigation and water conservancy facilities; increasing network compactness will increase the possibility of farmers’ participation in the supply; trust and commitment, social ethos and sense of belonging, social participation, and other factors have no significant influence on farmer participation behavior. It can be seen that network tightness and network scale play an important role in the behavior of farmers’ participation in public affairs. In conclusion, social network relationships will affect farmers’ participation in the supply of irrigation and water conservancy facilities, but different dimensions have different influences on it.