Update 2019/03/18
Use this plugin and guideline: https://sparxsystems.us/go/restapi/
Original answer
I'm using Enterprise Architect at this moment to model an API. For this projects you have users that are granted a budget to buy certain products. The model is not yet complete, but I'm adding it here as reference.
In EA I added some additional stereotypes: Path, Resource and Representation + a new datatype ParamQuery.
To model the API you create a new class diagram and start by the root of your API as a class of stereotype "Application". Next you add your Resources and Paths. For each Resource you add the necessary GET, POST, PUT etc. operations. If QueryParams are passed along in the string for the GET operations you add them as Parameters for the operation, but as type QueryParam (you need to create it the first time). For the messagebody of POST operations you add a parameter of the class type it represents.
Next you add the "representation" classes, used by the Resources.