The Invisible Man - H. G. Wells, 1897
This is a somewhat debatable one, but in discussing the process used to turn the protagonist invisible, Wells writes:
...the essential phase was to place the transparent object whose refractive index was to be lowered between two radiating centres of a sort of ethereal vibration, of which I will tell you more fully later. No, not those Röntgen vibrations—I don't know that these others of mine have been described. Yet they are obvious enough.
"Röntgen vibrations" refers to X-rays, which had been discovered only two years previously. Wells' protagonist got his invisibility "super power" by exposure to something that was in some way like X-rays, but different.
Perhaps, like X-rays, these "ethereal vibrations" were ionising. Or perhaps they weren't, we don't know. But in either case this seemed worth mentioning as a very early example of unusual abilities being associated with exposure to radiation.