Cesium doesn’t have anything like that built in. This pull request may help; it adds WMS GetCapabilities querying to Cesium:
You may also be interested in TerriaJS:
It’s an open source project (same license as Cesium) that I and others built originally for Australia’s National Map. It can query WMS (also WFS, WMTS, CKAN, ArcGIS Server, etc.) for their layers and display them in a catalog. It also has a 2D fallback (based on Leaflet) for systems that can’t run Cesium/WebGL, and some other niceties. To try out the WMS querying, visit:
Click Add Data in the top right, paste in your WMS URL, and click Add. As long as your WMS server supports CORS, the list of layers on the server will appear at the bottom of the “Data Catalogue”.