  We derive observational consequences of the hypothesis that cosmic rays
(CR's) of energy $>10^{19}eV$ originate in the same cosmological objects
producing gamma-ray bursts (GRB's). Inter-galactic magnetic fields $\gtrsim
10^{-12} G$ are required in this model to allow CR's to be observed
continuously in time by producing energy dependent delays in the CR arrival
times. This results in individual CR sources having very narrow observed
spectra, since at any given time only those CR's having a fixed time delay are
observed. Thus, the brightest CR sources should be different at different
energies. The average number of sources contributing to the total CR flux
decreases with energy much more rapidly than in a model of steady CR sources,
dropping to one at $E_{crit} \simeq2\times10^{20}$~eV with very weak
sensitivity to the inter-galactic magnetic field strength. Below $E_{crit}$, a
very large number of sources is expected, consistent with observations. Above
$E_{crit}$, a source may be observed with a flux considerably higher than the
time-averaged CR flux from all sources, if a nearby GRB occurred recently. If
such a source is present, its narrow spectrum may produce a ``gap'' in the
total spectrum. These signatures should be detectable by the planned ``Auger''
CR experiment.
