This article reports on the Design Science engineering cycle for implementing a modeling method to support model-driven, process-centric API management. The BPMN standard was hereby enriched on semantic, syntactic and tool levels in order to provide a viable solution for integrating API requests with diagrammatic business process models in order to facilitate the documentation or testing of REST API calls directly in a modeling environment. The method can be implemented by stakeholders that need to map and manage their API ecosystem, thus gaining more API management agility and improving their software engineering productivity. By assimilating API ecosystem conceptualization in the modeling environment, the proposal differs from both RPA (which typically employs non-BPMN process diagramming e.g., in UIPath) and BPM Systems (which typically isolate all API-related semantics outside the process modeling language to keep the diagrammatic representation standard-compliant).