Magnetic fields in turbulent, convective high-$beta$ plasma naturally develop highly tangled and complex topologies---the solar photosphere being the paradigmatic example. These fields are mostly undetectable by standard diagnostic techniques with finite spatio-temporal resolution due to cancellations of Zeeman polarization signals. Observations of resonance scattering polarization have been considered to overcome these problems. But up to now, observations of scattering polarization lack the necessary combination of high sensitivity and high spatial resolution in order to directly infer the turbulent magnetic structure at the resolution limit of solar telescopes. Here, we report the detection of clear spatial structuring of scattering polarization in a magnetically quiet solar region at disk center in the Sr~{sc i} 4607~AA~spectral line on granular scales, confirming theoretical expectations. We find that the linear polarization presents a strong spatial correlation with the local quadrupole of the radiation field. The result indicates that polarization survives the dynamic and turbulent magnetic environment of the middle photosphere and is thereby usable for spatially resolved Hanle observations. This is an important step toward the long-sought goal of directly observing turbulent solar magnetic fields at the resolution limit and investigating their spatial structure.