Ionizing radiation can be both charged particles and electromagnetic radiation. As pointed out in comments, a magnetic field can in some cases be used to deflect charged particles like protons and electrons, but not electromagnetic radiation like UV light, X-rays or gamma rays.
For ionizing charged particle radiation the Earth's magnetic field is low in strength, but very large (tens of thousands of kilometers) so it can do a pretty good job of slowing down and deflecting the charged particles in a coronal mass ejection or other sources. Some is deflected towards the Earth's poles and some passes around the Earth and continues into space.
But for us on Earth we also receive a major amount of shielding by the thickness of the Earth's atmosphere! The amount of atmospheric mass above us is about the same as being 10 meters under water (or 760 millimeters under mercury). This is why people who work in commercial aviation and spend a lot of time at cruise altitude receive more radiation than the rest of us.
For ionizing electromagnetic radiation such as gamma rays, X-rays, and ultraviolet light, magnetic fields by themselves do not provide any shield whatsoever. That only comes from the electrons and to some extent nuclei in the mass of Earth's atmosphere, or thick radiation shielding provided by concrete, rock, or water for example. The wavelengths are extremely small (shorter than visible light) and so the spacing between the wires of a Faraday cage would be huge in comparison, so no Faraday cage can work for ionizing EM radiation.
For non-ionizing electromagnetic radiation such as microwaves and radio waves, Faraday cages can work if the spacing between wires is smaller than a fraction of a wavelength of the EM radiation. So the metal grid in the window of a microwave oven allows us to see the food in visible light, but shields the outside from the microwaves inside.