Well, not in the way you think.
I recently found this video of an appearance of astronaut Scott Kelly on The Late Show with Stephen Colbert. During this segment, he talked about the fact that when he went to sleep on the Space Station and closed his eyes, he occasionally detected flashes of light. He attributed it to the cosmic radiation passing through his body, and his eyes in particular.
Check out the video at minute 3:30
My first inclination is to say that this is similar to how we detect neutrinos, i.e. the radiation particles interact with the medium in his yes, either the vitreous or the medium that makes up the lens, and this interaction causes the ejection of relativistic electron and subsequently, a Cerenkov radiation. The Cerenkov radiation is then detected by the eye.
Of course, there are other possibilities, such as the cosmic particle causes an excitation of an atom or molecules when they collided, and this then caused a light emission. But Scott Kelly mentioned that these flashes appeared like fireworks. So my guess here is that it is more of a very short cascade of events, and probably the Cerenkov light scenario.
This, BTW, is almost how we detect neutrinos, especially at Super Kamiokande and all the neutrino detectors around the world. Neutrinos come into the detector, and those that interact with the medium inside the detector (water, for example), cause the emission of relativistic electrons that move faster than the speed of light inside the medium. This creates the Cerenkov radiation, and typically, the light is blueish white. It's the same glow that you see if you look in a pool of fuel rods in a nuclear reactor.
So there! You can detect something with your eyes closed!