We observed the galaxy cluster CIZA J2242.8+5301 with the Sardinia Radio Telescope to provide new constraints on its spectral properties at high frequency. We conducted observations in three frequency bands centred at 1.4, 6.6 and 19 GHz, resulting in beam resolutions of 14, 2.9 and 1 arcmin, respectively. These single-dish data were also combined with archival interferometric observations at 1.4 and 1.7 GHz. From the combined images, we measured a flux density of S1.4 GHz = (158.3 ± 9.6) mJy for the central radio halo and S1.4 GHz = (126 ± 8) and (11.7 ± 0.7) mJy for the northern and the southern relics, respectively. After the spectral modelling of the discrete sources, we measured at 6.6 GHz S6.6 GHz = (17.1 ± 1.2) and (0.6 ± 0.3) mJy for the northern and southern relics, respectively. Assuming simple diffusive shock acceleration, we interpret measurements of the northern relic with a continuous injection model represented by a broken power law. This yields an injection spectral index αinj = 0.7 ± 0.1 and a Mach number M = 3.3 ± 0.9, consistent with recent X-ray estimates. Unlike other studies of the same object, no significant steepening of the relic radio emission is seen in data up to 8.35 GHz. By fitting the southern relic spectrum with a simple power law (Sν ∝ ν-α), we obtained a spectral index α ≈ 1.9 corresponding to a Mach number (M ≈ 1.8) in agreement with X-ray estimates. Finally, we evaluated the rotation measure of the northern relic at 6.6 GHz. These results provide new insights on the magnetic structure of the relic, but further observations are needed to clarify the nature of the observed Faraday rotation.