  We introduce Weyl Josephson circuits: small Josephson junction circuits that
simulate Weyl band structures. We first formulate a general approach to design
circuits that are analogous to Bloch Hamiltonians of a desired dimensionality
and symmetry class. We then construct and analyze a six-junction device that
produces a 3D Weyl Hamiltonian with broken inversion symmetry and in which
topological phase transitions can be triggered \emph{in situ}. We argue that
currently available superconducting circuit technology allows experiments that
probe topological properties inaccessible in condensed matter systems.
