We investigate how the imprint of Faraday rotation on radio spectra can be used to determine the geometry of radio sources and the strength and structure of the surrounding magnetic fields. We model spectra of Stokes Q and U for frequencies between 200 MHz and 10 GHz for Faraday screens with large-scale or small-scale magnetic fields external to the source. These sources can be uniform or 2D Gaussians on the sky with transverse linear gradients in rotation measure (RM), or cylinders or spheroids with an azimuthal magnetic field. At high frequencies, the spectra of all these models can be approximated by the spectrum of a Gaussian source; this is independent of whether the magnetic field is large scale or small scale. A sinc spectrum in polarized flux density is not a unique signature of a volume where synchrotron emission and Faraday rotation are mixed. A turbulent Faraday screen with a large field coherence length produces a spectrum which is similar to the spectrum of a partial coverage model. At low and intermediate frequencies, such a Faraday screen produces a significantly higher polarized signal than Burn's depolarization model, as shown by a random walk model of the polarization vectors. We calculate RM spectra for four frequency windows. Sources are strongly depolarized at low frequencies, but RMs can be determined accurately if the sensitivity of the observations is sufficient. Finally, we show that RM spectra can be used to differentiate between turbulent foreground models and partial coverage models.