  We construct a map of deflections of ultra-high energy cosmic rays by
extragalactic magnetic fields using a magneto-hydrodynamical simulation of
cosmic structure formation that realistically reproduces the positions of known
galaxy clusters in the Local Universe. Large deflection angles occur in cluster
regions, which however cover only an insignificant fraction of the sky. More
typical deflections of order $\lsim 1^\circ$ are caused by crossings of
filaments. For protons with energies $E \geq 4 \times 10^{19} {\rm eV}$,
deflections do not exceed a few degrees over most of the sky up to a
propagation distance of 500 Mpc. Given that the field strength of our simulated
intergalactic magnetic field forms a plausible upper limit, we conclude that
charged particle astronomy is in principle possible.
