Aims: We investigated the magnetic properties of radio relics located at the peripheries of galaxy clusters at high radio frequencies, where the emission is expected to be free of Faraday depolarization. The degree of polarization is a measure of the magnetic field compression and, hence, the Mach number. Polarization observations can also be used to confirm relic candidates. Methods: We observed three radio relics in galaxy clusters and one radio relic candidate at 4.85 and 8.35 GHz in total emission and linearly polarized emission with the Effelsberg 100-m telescope. In addition, we observed one radio relic candidate in X-rays with the Chandra telescope. We derived maps of polarization angle, polarization degree, and Faraday rotation measures. Results: The radio spectra of the integrated emission below 8.35 GHz can be well fitted by single power laws for all four relics. The flat spectra (spectral indices of 0.9 and 1.0) for the so-called Sausage relic in cluster CIZA J2242 53 and the so-called Toothbrush relic in cluster 1RXS 06 42 indicate that models describing the origin of relics have to include effects beyond the assumptions of diffuse shock acceleration. The spectra of the radio relics in ZwCl 0008 52 and in Abell 1612 are steep, as expected from weak shocks (Mach number ?2.4). Polarization observations of radio relics offer a method of measuring the strength and geometry of the shock front. We find polarization degrees of more than 50% in the two prominent Mpc-sized radio relics, the Sausage and the Toothbrush, which are among the highest percentages of linear polarization detected in any extragalactic radio source to date. This is remarkable because the large beam size of the Effelsberg single-dish telescope corresponds to linear extensions of about 300 kpc at 8.35 GHz at the distances of the relics. The high degree of polarization indicates that the magnetic field vectors are almost perfectly aligned along the relic structure, as expected for shock fronts that are observed edge-on. The polarization degrees correspond to Mach numbers of >2.2. Polarized emission is also detected in the radio relics in ZwCl 0008 52 and, for the first time, in Abell 1612. The smaller sizes and lower degrees of polarizations of the latter relics indicate a weaker shock and/or an inclination between the relic and the sky plane. Abell 1612 shows a complex X-ray surface brightness distribution, indicating a recent major merger and supporting the classification of the radio emission as a radio relic. In our cluster sample, no wavelength-dependent Faraday depolarization is detected between 4.85 GHz and 8.35 GHz, except for one component of the Toothbrush relic. Faraday depolarization between 1.38 GHz and 8.35 GHz varies with distance from the center of the host cluster 1RXS 06 42, which can be explained by a decrease in electron density and/or in strength of a turbulent (or tangled) magnetic field. Faraday rotation measures show large-scale gradients along the relics, which cannot be explained by variations in the Milky Way foreground. Conclusions: Single-dish telescopes are ideal tools to confirm relic candidates and search for new relic candidates. Measurement of the wavelength-dependent depolarization along the Toothbrush relic shows that the electron density of the intra-cluster medium (ICM) and strength of the tangled magnetic field decrease with distance from the center of the foreground cluster. Large-scale regular fields appear to be present in intergalactic space around galaxy clusters. Based on observations with the 100-m telescope at Effelsberg, operated by the Max-Planck-Institut für Radioastronomie (MPIfR) on behalf of the Max-Planck-Gesellschaft.The reduced Stokes parameter images (FITS files) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A A/600/A18
