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Observations of scattering polarization and the Hanle effect in various spectral lines are increasingly used to complement traditional solar magnetic field determination techniques. One of the strongest scattering polarization signals in the photosphere is measured in the Sr I line at 4607.3 Å when observed close to the solar limb. Here, we present the first observational evidence of Hanle rotation in the linearly polarized spectrum of this at several limb distances. We observed with the Zurich IMaging POLarimeter, ZIMPOL, at the IRSOL observatory, with exceptionally good seeing conditions, allowing for long integration times. We combined the fast modulating polarimeter with a slow modulator installed in front of the telescope. This combination allows the measurement of spectropolarimetric data being highly precise and unprecedentedly accurate. Fixing the reference direction for positive Stokes $Q$ parallel to the limb, we detect singly-peaked $U/I$ signals well above the noise level. We can exclude instrumental origin for such $U/I$ signals. These signatures are exclusively found in the Sr I line, but not in the adjoining Fe I line, therefore eliminating the Zeeman effect as the mechanism responsible for their appearance. However, we find a clear spatial correlation between the circular polarization produced by the Zeeman effect and the $U/I$ amplitudes. This suggests that the detected $U/I$ signals are the signatures of Hanle rotation caused by a spatially resolved magnetic field. A novel measurement technique allows for determining the absolute level of polarization with unprecedented precision. Using this technique, high-precision spectropolarimetric observations reveal for the first time unambiguous $U/I$ signals due to Hanle rotation in the Sr I line.