I think you should use some 3d party server to support the JWT token and there is no out of the box JWT support in WEB API 2.
However there is an OWIN project for supporting some format of signed token (not JWT). It works as a reduced OAuth protocol to provide just a simple form of authentication for a web site.
You can read more about it e.g. here.
It's rather long, but most parts are details with controllers and ASP.NET Identity that you might not need at all. Most important are
Step 9: Add support for OAuth Bearer Tokens Generation
Step 12: Testing the Back-end API
There you can read how to set up endpoint (e.g. "/token") that you can access from frontend (and details on the format of the request).
Other steps provide details on how to connect that endpoint to the database, etc. and you can chose the parts that you require.