  We investigate the influence of Pearl vortices in the vicinity of an
edge-type Josephson junction for a superconducting thin-film loop in the form
of an annulus, under uniform magnetic field. Specifically, we obtain the exact
analytic formulation that allows to describe the circulating current density
and the gauge invariant phase increment $\Delta\phi$ across the junction. The
main properties of $\Delta\phi$ and their influence on the critical current
pattern $I_c(B)$ are described quantitatively in terms of the loop's width to
radius ratio $W/R$ and of the vortex position within the loop ${\bf r}_v$. It
is shown that narrow loops ($W/R < 0.3$) may be well described by the straight
geometry limit. However, such approximation fails to predict a number of
distinctive features captured by our formulation, as the node lifting effect of
the $I_c(B)$ pattern in wide loops or the actual influence of a vortex pinned
at different positions.
