Charged particle will make charge separation along it's path (ionization). This will cause malicious (wrong) chemical reactions occur in body, including DNA damage. The effect of these chemical reactions depend on their amount. Low amount can be self cured, while high amount will cause radiation sickness and probably death.

This can be calculated, but also deduced by comparison.

One single proton from `LHC` has 4 TeV of energy. This is much less than probable energy of cosmic rays protons. 

![enter image description here][1]

According this plot, 4 TeV protons come onto each square meter approximately each month. One per year it come protons of 10E16 eV, i.e. 10000 times harder, than from `LHC`.

Cosmic ray protons hardly reach ground but they can reach astronauts. No any damage of single protons on astronauts registered. Some of astronauts report rare unusual light flashes in their eyes which may be caused by particles penetrating they brains or retina.

P.S. Also regard answer about BEAM of particles, which can definitely damage the body.

 [1]: https://i.sstatic.net/7hCnE.png