  Radio galaxies are intensively discussed as the sources of cosmic rays
observed above about $3\,{\times}\,10^{18}\,\text{eV}$, called ultra-high
energy cosmic rays (UHECRs). We present a first, systematic approach that takes
the individual characteristics of these sources into account, as well as the
impact of the extragalactic magnetic-field structures up to a distance of 120
Mpc. We use a mixed simulation setup, based on 3D simulations of UHECRs ejected
by observed, individual radio galaxies taken out to a distance of 120 Mpc, and
on 1D simulations over a continuous source distribution contributing from
beyond 120 Mpc. Additionally, we include the ultra-luminous radio galaxy Cygnus
A at a distance of about $250\,$Mpc, as its contribution is so strong that it
must be considered as an individual point source. The implementation of the
UHECR ejection in our simulation setup is based on a detailed consideration of
the physics of radio jets and standard first-order Fermi acceleration. We show
that the average contribution of radio galaxies taken over a very large volume
cannot explain the observed features of UHECRs measured at Earth. However, we
obtain excellent agreement with the spectrum, composition, and
arrival-direction distribution of UHECRs measured by the Pierre Auger
Observatory, if we assume that most UHECRs observed arise from only two
sources: The ultra-luminous radio galaxy Cygnus A, providing a mostly light
composition of nuclear species dominating up to about
$6\,{\times}\,10^{19}\,$eV, and the nearest radio galaxy Centaurus A, providing
a heavy composition dominating above $6\,{\times}\,10^{19}\,$eV. Here we have
to assume that extragalactic magnetic fields out to 250 Mpc, which we did not
include in the simulation, are able to isotropize the UHECR events at about 8
EeV arriving from Cygnus A.
