Different from the data sparsity that traditional recommendations suffer from, context-aware recommender systems (CARS) face specific sparsity challenges related to contextual features, i.e., feature sparsity and interaction sparsity. How knowledge graphs address these challenges remains under-discussed. To bridge this gap, in this paper, we first propose a novel pairwise intent graph (PIG) containing nodes of users, items, entities, and enhanced intents to integrate knowledge graphs into CARS efficiently. Enhanced intent nodes are generated through the specific fusion of relational sub-intent and contextual sub-intent, and they are derived from semantic information and contextual information, respectively. We develop a pairwise intent graph embedding learning (PING) framework based on it. Specifically, our PING uses a pairwise intent joint graph convolution module to obtain refined embedding of all the features, where each enhanced intent node acts as a hub to effectively propagate information among different features and between all the features and knowledge graphs. Then, a recommendation module with refined embeddings is used to replace the randomly initialized embeddings of downstream recommendation models to improve model performance. Extensive experiments on three public datasets and some real-world scenarios verify the effectiveness and compatibility of our PING.