A charged particle will create charge separation (ionization) along its path. This will cause harmful chemical reactions to occur in the body, including DNA damage. The effects of these chemical reactions depend on their amount. The body can heal from a low amount on its own, while a high amount will cause radiation sickness and probably death.
This can be calculated, but also deduced by comparison.
A single proton from
LHC has 4 TeV of energy. This is much less than the probable energy of cosmic rays' protons.
According this plot, approximately four TeV protons hit each square meter each month. Once per year, they are protons of 10E16 eV, i.e. 10000 times harder, than those from
Cosmic ray protons hardly ever reach Earth's surface but astronauts can be exposed to them. No damage to astronauts from individual protons has been registered. Some astronauts report rare unusual light flashes in their eyes which may be caused by particles penetrating their brains or retinas.
P.S. Also see the answer about BEAMS of particles, which can definitely damage the body.