hard ceramic? They're often confused, though they are completely different. Tungsten metal is used in lightbulb filaments and for TIG electrodes........ Tungsten carbide (WC) on the other hand is used for sawblades, concrete drills, and machine tools.
In regards to metallic tungsten you might be able to do so if the part was really thin, or really small. I think you'd be kind of limited by the realistic amount of heat input you can get with TIG without the heat simply being dissipated by conduction. The hotter the temp required the more quickly heat is lost by conduction. You might compare this to trying to weld 1/2" plate with an oxyacetylene torch. The heat is simply not intense enough.
As you know tungsten metal has the second highest melting point of any material, after carbon. (graphite evaporates like dry ice instead of melting.)
Electron beam welding might work. Solid state friction welding might work too, but you'd still have to get it insanely hot.
Technically, tungsten carbide, is a metal-matrix composite. It's made up of carbide powder bonded with pure cobalt or nickel. This makes it easy to fabricate into odd shapes. You attach it to a saw blade, for example, by silver brazing. I've done it before. The stuff is still too brittle to be directly welded.