  The existence of fast radio bursts (FRBs), a new type of extragalatic
transients, has been established recently and quite a few models have been
proposed. In this work we discuss the possible connection between the FRB
sources and ultra-high energy ($>10^{18}$ eV) cosmic rays. We show that in the
blitzar model and the model of merging binary neutron stars, the huge energy
release of each FRB central engine together with the rather high rate of FRBs,
the accelerated EeV cosmic rays may contribute significantly to the observed
ones. In other FRB models including for example the merger of double white
dwarfs and the energetic magnetar radio flares, no significant EeV cosmic ray
is expected. We also suggest that the mergers of double neutron stars, even if
they are irrelevant to FRBs, may play a non-ignorable role in producing EeV
cosmic ray protons if supramassive neutron stars were formed in a good fraction
of mergers and the merger rate is $\gtrsim 10^{3}~{\rm yr^{-1}~ Gpc^{-3}}$.
Such a possibility will be unambiguously tested in the era of gravitational
wave astronomy.
