Define obsolete.
If you consider that it's used for Classic ASP.NET, with WebForms and stuff like that, we can say yes.
But it is still considered a valid and supported component in .NET. You can use it.
The question is whether it should. There are no updates on top of it, and there is a general, not exactly official, recommendation not to use it anymore.
Anyone who has a large base using it may have some gain maintaining continuity. If you're going to just consume what already exists, it might be interesting.
If there is little and it is easy to convert I think I would of Web API using ASP.NET Core. Only you can judge whether you compensate for the effort. The gain will not be great in use, perhaps more organization in development, or scale.