  We measured the dipole of the diffuse $\gamma$-ray background (DGB)
identifying a highly significant time-independent signal coincidental with that
of the Pierre Auger UHECR. The DGB dipole is determined from flux maps in
narrow energy bands constructed from 13 years of observations by the Large Area
Telescope (LAT) of the {\it Fermi} satellite. The $\gamma$-ray maps were
clipped iteratively of sources and foregrounds similar to that done for the
cosmic infrared background. The clipped narrow energy band maps were then
assembled into one broad energy map out to the given energy starting at
$E=2.74$ Gev, where the LAT beam falls below the sky's pixel resolution. Next
we consider cuts in Galactic latitude and longitude to probe residual
foreground contaminations from the Galactic Plane and Center. In the broad
energy range $2.74 < E\leq115.5$ GeV the measured dipoles are stable with
respect to the various Galactic cuts, consistent with an extragalactic origin.
The $\gamma$-ray sky's dipole/monopole ratio is much greater than that expected
from the DGB clustering component and the Compton-Getting effect origin with
reasonable velocities. At $\simeq (6.5-7)\%$ it is similar to the Pierre Auger
UHECRs with $E_{\rm UHECR}\ge 8$ EeV pointing to a common origin of the two
dipoles. However, the DGB flux associated with the found DGB dipole reaches
parity with that of the UHECR around $E_{\rm UHECR}\le 1$ EeV, perhaps arguing
for a non-cascading mechanism if the DGB dipole were to come from the higher
energy UHECRs. The signal/noise of the DGB dipole is largest in the $5-30$ GeV
range, possibly suggesting the $\gamma$-photons at these energies are the ones
related to cosmic rays.
