We report experimental measurements of the dynamical polarizability of dysprosium, at a wavelength of 532 nm. We measure all three components (scalar, vector, tensor) of the anisotropic polarizability for the ground and the excited manifolds of the intercombination transition of Dy at 626 nm. The apparatus on which the measurements are performed is first presented. We obtain with this setup imaging of single Dy atoms with fidelity above 99 % and losses below 2.5 % induced by imaging. We then describe the methods used to extract the polarizability. In particular, we combine a measurement of trap frequency and trap depth on single atoms in optical tweezers, allowing us to obtain a measurement of the ground state polarizability free of errors in trap waist calibration. The obtained values give a magic condition between two Zeeman states in the ground and excited manifolds, which was used to image single atoms in optical tweezer arrays. The scalar polarizability of the ground state is in disagreement with theoretical expectations, calling for future investigations to resolve the discrepancy.