The Fermi surface of a conventional two-dimensional electron gas is equivalent to a circle, up to smooth deformations that preserve the orientation of the equi-energy contour. Here we show that a Weyl semimetal confined to a thin film with an in-plane magnetization and broken spatial inversion symmetry can have a topologically distinct Fermi surface that is twisted into a $mbox{figure-8}$ $-$ opposite orientations are coupled at a crossing which is protected up to an exponentially small gap. The twisted spectral response to a perpendicular magnetic field $B$ is distinct from that of a deformed Fermi circle, because the two lobes of a mbox{figure-8} cyclotron orbit give opposite contributions to the Aharonov-Bohm phase. The magnetic edge channels come in two counterpropagating types, a wide channel of width $beta l_m^2propto 1/B$ and a narrow channel of width $l_mpropto 1/sqrt B$ (with $l_m=sqrt{hbar/eB}$ the magnetic length and $beta$ the momentum separation of the Weyl points). Only one of the two is transmitted into a metallic contact, providing unique magnetotransport signatures.
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