We present a new approach that demonstrates the deflection and guiding of relativistic electron beams over curved paths by means of the magnetic field generated in a plasma-discharge capillary. We experimentally prove that the guiding is much less affected by the beam chromatic dispersion with respect to a conventional bending magnet and, with the support of numerical simulations, we show that it can even be made dispersionless by employing larger discharge currents. This proof-of-principle experiment extends the use of plasma-based devices, that revolutionized the field of particle accelerators enabling the generation of GeV beams in few centimeters. Compared to state-of-the-art technology based on conventional bending magnets and quadrupole lenses, these results provide a compact and affordable solution for the development of next-generation tabletop facilities.