(My answer seems to differ from the earlier ones that @dmckee aptly pointed out, so I'll go ahead and risk posting it. My main difference is that I suspect that a head on collision with a large nucleus could produce a wide enough horizontal-splatter radiation cone to produce a fatal event.)
Since the 1991 Oh-My-God particle was most likely a proton and had the kinetic energy of a fast baseball, I'm going out on a limb and saying yes, you could be killed by a single particle. This Harvard physics site suggests an approximate energy transfer of about 0.2% in transfers with heavy nuclei, which as I discuss below may be enough to do you in with that kind of particle. But it would be the ensuing radiation event and cone that would do you in, not the kinetic energy of the particle.
The main issue is that your head doesn't have anything in it remotely solid enough to stop or even slow down a particle with that much momentum. So, like a locomotive passing through a cloud of fog, it's going to zip through pretty much as if your head isn't there.
The question, then, is to ask not what the fog will do to the locomotive, but what the locomotive will do to the fog -- that fog being your head.
Even a single solid, exactly head-on collision with a nice fat iron nucleus just as an ultra cosmic ray proton enters your head would probably not be a pretty event in terms of the resulting secondary radiation shower. I'm guessing (nothing more, I haven't tried to calculate anything) that outward splattering as iron nucleus components symmetrically vaporize into a nice little quark plasma or whatever that kind of power produces (I don't think anyone really knows for sure; it's way outside of our league on earth) would produce a wide enough cone of particle-zoo consequences to fry your brain nicely. That's especially true if you really can get as high as 1/500 energy transfer, in which case we might well be talking about, er, rapid heating events that would be a bit more spectacular (and way more gruesome) than simply falling over dead.
And the odds on such an event? Almost unbelievably low. Look at the date on the Oh-My-God particle: 1991. We haven't seen one since, and it was a high-atmosphere event that most certainly did not hit someone in the head. As @dmckee aptly notes, ordinary cosmic rays or their secondary outputs hit us all the time, and astronauts watch direct collision buzz through their retinas without much harm.