To actually answer OP's question, I don't think any "classical" antenna design could get close to ionizing radiation. I'm not an expert on radio tech, but as far as I know even ~1THz antennae are experimental and extremely hard to work with. Getting to ionizing radiation is another factor of at least 1000 in frequency and size.
Not to mention that the plasma frequency of most metals is somewhere near the optical spectrum, and my guess is that would make it impossible to use them as antennae even if you could solve the technical challenges.
Maybe more exotic antenna variations could work in principle, but they'd be incredibly difficult to build.
