Faraday rotation is one of the most widely used observables to infer the strength and configuration of the magnetic field in the ionised gas of the Milky Way and nearby spiral galaxies. Here we compute synthetic Faraday rotation maps at $z=0$ for a set of disk galaxies from the Auriga high-resolution cosmological simulations, for different observer positions within and outside the galaxy. We find that the strength of the Faraday rotation of our simulated galaxies for a hypothetic observer at the solar circle is broadly consistent with the Faraday rotation seen for the Milky Way. The same holds for an observer outside the galaxy and the observed signal of the nearby spiral galaxy M51. However, we also find that the structure and angular power spectra of the synthetic all-sky Faraday rotation maps vary strongly with azimuthal position along the solar circle. We argue that this variation is a result of the structure of the magnetic field of the galaxy that is dominated by an azimuthal magnetic field ordered scales of several kpc, but has radial and vertical magnetic field components that are only ordered on scales of 1-2 kpc. Because the magnetic field strength decreases exponentially with height above the disk, the Faraday rotation for an observer at the solar circle is dominated by the local environment. This represents a severe obstacle for attempts to reconstruct the global magnetic field of the Milky Way from Faraday rotation maps alone without including additional observables.

10 pages, 10 figures, accepted by MNRAS