  Weyl semimetals are a three dimensional topological phase of matter with
linearly dispersed Weyl points which appear in pairs and carry opposite
chirality. The separation of paired Weyl points allows charge transfer between
them in the presence of parallel electric and magnetic fields, which is known
as the chiral anomaly. In this paper, we theoretically study the influence of
the chiral anomaly induced chiral charge imbalance on the Josephson current in
a Weyl superconductor-Weyl semimetal-Weyl superconductor junction. In Weyl
superconductors, two types of pairings are considered, namely, zero momentum
BCS-like pairing and finite momentum FFLO-like pairing. For BCS-like pairing,
we find that the Josephson current exhibits $0$-$\pi$ transitions and
oscillates as a function of $\lambda_{0} L $, where $\lambda_{0}$ is the
chirality imbalance induced by the parallel electric and magnetic fields and
$L$ is the length of the Weyl semimetal. The amplitude of the Josephson current
also depends on the angle $\beta$ between the line connecting two paired Weyl
points and the transport direction along the junction. For FFLO-like pairing,
the chirality imbalance induced periodic oscillations are absent and the
Josephson current is also independent of the angle $\beta$. These findings are
useful in detecting the chiral anomaly and distinguishing the superconducting
pairing mechanism of Weyl semimetals.
