  We investigate the production of ultra-high-energy cosmic ray (UHECR) in jets
from low-luminosity active galactic nuclei (LLAGN). We propose a model for the
UHECR contribution from the spin-down power of black holes (BHs) in LLAGN,
which present a jet power $P_{\mathrm{j}} \leqslant 10^{46}$ erg s$^{-1}$. This
is in contrast to the opinion that only high-luminosity AGN can accelerate
particles to energies $ \geqslant 50$ EeV. We rewrite the equations which
describe the synchrotron self-absorbed emission of a non-thermal particle
distribution to obtain the observed radio flux density from flat-spectrum core
sources and its relationship to the jet power. In general, the jet power
provides the UHECR luminosity and so, its relationship to the observed radio
flux density. We found that the UHECR luminosity is dependent on the observed
radio flux density, the distance to the AGN, and the BH mass, where the
particle acceleration regions can be sustained by the magnetic energy
extraction from spinning BHs and where the strength of the magnetic field at
the sites of particle acceleration scales with the maximum value of the BH
magnetic field, which is $\sim 10^4$ gauss for a BH of $10^9 M_{\odot}$. We
apply the model to M87 and Cen A, two possible sources of UHECRs, whose jet
parameters can be inferred from observational data. Next, we use a complete
sample of 29 steep spectrum radio sources with a total flux density greater
than 0.5 Jy at 5 GHz to make predictions for the maximum particle energy,
luminosity, and flux of the UHECRs from nearby AGN. Using our proposed model,
it is possible to show that LLAGN can be sites of the origin of UHECRs. In
additional, the scenario in which the contribution to the UHECR flux from many
weak radio galaxies would dominate over that from a few strong radio galaxies,
or vice-versa, should be substantiated with further statistics.
