Abstract Supernova remnants are commonly considered to produce most of the Galactic cosmic rays via diffusive shock acceleration. However, many questions regarding the physical conditions at shock fronts, such as the magnetic-field morphology close to the particle acceleration sites, remain open. Here we report the detection of a localized polarization signal from some synchrotron X-ray emitting regions of Tycho’s supernova remnant made by the Imaging X-ray Polarimetry Explorer. The derived degree of polarization of the X-ray synchrotron emission is 9% ± 2% averaged over the whole remnant, and 12% ± 2% at the rim, higher than the value of polarization of 7%–8% observed in the radio band. In the west region, the degree of polarization is 23% ± 4%. The degree of X-ray polarization in Tycho is higher than for Cassiopeia A, suggesting a more ordered magnetic field or a larger maximum turbulence scale. The measured tangential direction of polarization corresponds to the radial magnetic field, and is consistent with that observed in the radio band. These results are compatible with the expectation of turbulence produced by an anisotropic cascade of a radial magnetic field near the shock, where we derive a magnetic-field amplification factor of 3.4 ± 0.3. The fact that this value is significantly smaller than those expected from acceleration models is indicative of highly anisotropic magnetic-field turbulence, or that the emitting electrons either favor regions of lower turbulence, or accumulate close to where the orientation of the magnetic field is preferentially radially oriented due to hydrodynamical instabilities.