Over two decades, context awareness has been incorporated into recommender systems in order to provide, not only the top-rated items to consumers but also the ones that are suitable to the user context. As a class of context-aware systems, context-aware service recommendation (CASR) aims to bind high-quality services to users, while taking into account their context requirements, including invocation time, location, social profiles, connectivity, and so on. However, current CASR approaches are not scalable with the huge amount of service data (QoS and context information, users reviews and feedbacks). In addition, they lack a rich representation of contextual information, as they adopt a simple matrix view. Moreover, current CASR approaches adopt the traditional user-service relation and they do not allow for multi-relational interactions between users and services in different contexts. To offer a scalable and context-sensitive service recommendation with great analysis and learning capabilities, we provide a rich and multi-relational representation of the CASR knowledge, based on the concept of knowledge graph. The constructed context-aware service knowledge graph (C-SKG) is, then, transformed into a low-dimensional vector space to facilitate its processing. For this purpose, we adopt Dilated Recurrent Neural Networks to propose a context-aware knowledge graph embedding, based on the principles of first-order and subgraph-aware proximity. Finally, a recommendation algorithm is defined to deliver the top-rated services according to the target user's context. Experiments have proved the accuracy and scalability of our solution, compared to state-of-the-art CASR approaches.