One of the key research problems in stellar physics is to decipher the small-scale magnetic activity of the quiet solar atmosphere. Recent magneto-convection simulations that account for small-scale dynamo action have provided three-dimensional (3D) models of the solar photosphere characterized by a high degree of small-scale magnetic activity, similar to that found through theoretical interpretation of the scattering polarization observed in the Sr I 4607 Å line. Here we present the results of a novel investigation of the Hanle effect in this resonance line based on 3D radiative transfer calculations in a high-resolution magneto-convection model having most of the convection zone magnetized close to the equipartition and a surface mean field strength < B>≈ 170 G. The Hanle effect produced by the model’s magnetic field depolarizes the zero-field scattering polarization signals significantly, to the extent that the center-to-limb variation (CLV) of the calculated spatially averaged polarization amplitudes is compatible with the observations. The standard deviation of the horizontal fluctuations of the calculated scattering polarization signals is very sensitive to the model’s magnetic field, and we find that the predicted spatial variations are sufficiently sizable so as to be able to detect them, especially with the next generation of solar telescopes. We find that at all on-disk positions, the theoretical scattering polarization signals are anticorrelated with the continuum intensity. To facilitate reaching new observational breakthroughs, we show how the theoretically predicted polarization signals and spatial variations are modified when deteriorating the signal-to-noise ratio and the spectral and spatial resolutions of the simulated observations.