Electronic transport measurements in a magnetic field on the topological Dirac semimetal Cd3As2 identify the predicted Weyl orbits that weave Fermi arcs and bulk states together; the Weyl orbits enable transfer of chirality from one node to another, and open up the possibility of controlling topological properties electronically. In recently discovered topological semimetals, quasiparticles appear that are condensed-matter versions of high-energy massless Weyl fermions. They show curious electronic behaviour, having a distinct chirality and residing in topologically protected states. At the surface, so-called Fermi arcs form between specific Weyl nodes, and these have recently been observed in spectroscopic measurements. Philip Moll et al. present electronic transport measurements of the topological Dirac semimetal Cd3As2 in a magnetic field, identifying the predicted Weyl orbits that weave Fermi arcs and bulk states together. These Weyl orbits enable transfer of chirality from one node to another and open up the possibility of controlling topological properties electronically. The dispersion of charge carriers in a metal is distinctly different from that of free electrons owing to their interactions with the crystal lattice. These interactions may lead to quasiparticles mimicking the massless relativistic dynamics of high-energy particle physics1,2,3, and they can twist the quantum phase of electrons into topologically non-trivial knots—producing protected surface states with anomalous electromagnetic properties4,5,6,7,8,9. These effects intertwine in materials known as Weyl semimetals, and in their crystal-symmetry-protected analogues, Dirac semimetals10. The latter show a linear electronic dispersion in three dimensions described by two copies of the Weyl equation (a theoretical description of massless relativistic fermions). At the surface of a crystal, the broken translational symmetry creates topological surface states, so-called Fermi arcs11, which have no counterparts in high-energy physics or conventional condensed matter systems. Here we present Shubnikov–de Haas oscillations in focused-ion-beam-prepared microstructures of Cd3As2 that are consistent with the theoretically predicted 'Weyl orbits', a kind of cyclotron motion that weaves together Fermi-arc and chiral bulk states12. In contrast to conventional cyclotron orbits, this motion is driven by the transfer of chirality from one Weyl node to another, rather than momentum transfer of the Lorentz force. Our observations provide evidence for direct access to the topological properties of charge in a transport experiment, a first step towards their potential application.