Well, yes, but you're going to have to decide if it's worth the effort for you.
When you say Tungsten Carbide, I think you mean Tungsten Carbide (WC). Pure Tungsten Carbide is an intermetallic, so doesn't have the soft, tough properties of a metal - it is halfway to a ceramic. The material has fewer "slip planes" available to it because of the large difference in atomic diameters between tungsten and carbon. Consequently, attempting to form it at room temperature will only result in cracking. Raising the temperature is a little better (assuming it was pure tunsten), but still with the reduced slip planes the material will crack even with hot forging.
The way around this? It turns out if you can support the material in a tri-axial compression state (i.e., compressed in 3 dimensions), the compression will keep any cracks that are attempting to form, closed, and you can then hot forge the material.
What is a practical way to do this? Cast steel around the tungsten carbide, and then heat up the entire casting to just below the melting point of steel, and hot roll form the assembly. The tungsten carbide will be supported on all sides by the steel, keeping the tunsten carbide compressed and supported against cracking. After forming, the steel can be dissolved in hydrochloric acid and the tunsten carbide parts will be available at the bottom of the acid tank.
I understand there are some specialized hot pressing/extrusion setups that can do limited forming - these usually start with powdered metals, press, then sinter, the extrude, all at very high temperatures.
Pure tungsten for light bulb filaments had a similar problem. The early researchers had to form tungsten filaments by the casting method mentioned above, because they didn't understand why the pure tungsten metal could not be drawn into a filament. It turns out there was residual oxygen left over in the tungsten manufacturing process. This oxygen formed an intermetallic oxide (WO), and cause the same problem in forming as tungsten carbide (WC). By removing the oxygen level to below 20ppm, the oxygen wasn't available to tie up the slip planes, and the pure tungsten metal became soft enough to be able to be drawn into wires, then filaments, with suitable process annealing steps.
The trick then was to coordinate the drawing reduction/increase in cold working hardness and the process anneals in a clever way to recrystallize the tungsten metal grains into an elongated, but large shape (almost a single crystal), right after the last drawing step. When the filament is heated up in service, it recrystallizes into its final form: large elongated grains. It turns out that large elongated grains give the best strength at the very high temperatures that filaments operate at.
Pure metallic tungsten is a heavy and brittle metal (at room temperature). At operating temperatures it is softer, but most filaments are operated very near to tungsten's melting point. Tungsten is progressively drawn through diamond dies into finer wires. Note that drawing through a die puts the metal into both a compressive (reduction in diameter in the die) and tensile mode (the wire being pulled through the die). At least there is some compressive stress keeping the exterior from cracking (mostly through die design). If you attempted to forge the metal without regard to putting the material in compression, it is likely you would have problems with cracking.
Tungsten is a reactive metal at high temperatures, so you would want to keep the hot forging in a vacuum, or at least an inert atmosphere.
There are other intermetallics that are a little easier to form, especially those that don't have such large differences in diameter. Titanium aluminide (used in jet engine afterburners) is one. It can be formed/forged at relatively lower temperatures (say, 1800掳F).
You didn't say what your application was, so it is hard to be more specific. The tools required to do this are expensive, so most likely you'll want to work with someone who is already in the business.