Electromagnetic waves (light, radio, x-rays, etc) don’t need a medium to travel in. This is different from all of the other waves (sound, earthquakes, gravitational) and that is why scientists thought the universe must be full of a medium called aether and light propagated through that.
Eventually quantum physics proved that you don’t need a medium, as well as many other crazy ideas.
A radio signal is a wave* in the electric and magnetic fields that permeate all of space. They don’t need matter to propagate a wave, they are their own thing that just is.
You detect the disturbance in the fields by the way they wiggle matter with an electric charge (or a magnetic moment) back and forth, but the disturbance exists independently of whether or not there is matter to wiggle.
* More specifically, a pair of mutually reinforcing waves, but that’s unnecessary detail in the context of the question you asked
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