Axion-like particles (ALPs) are very light, neutral, spin zero bosons predicted by many theories which try to extend and complete the standard model of elementary particles. ALPs interact primarily with two photons and can generate photon-ALP oscillations in the presence of an external magnetic field. They are attracting increasing interest since photon-ALP oscillations produce deep consequences in astrophysics particularly in the very-high-energy (VHE) band, where they increase the transparency of the Universe to VHE photons by partially preventing absorption caused by the extragalactic background light. Furthermore, ALPs explain why photons coming from flat spectrum radio quasars (a particular class of active galactic nuclei, AGN) have been observed for energies above 20 GeV -which represents a first hint for the existence of an ALP. In addition, ALPs solve an anomalous redshift dependence of blazar (an AGN class) spectra -which represents a second hint for the existence of an ALP. In this paper, we study another effect of the photon-ALP interaction: the change of the polarization state of photons. In particular, we study the propagation of the photon-ALP beam starting where photons are produced -we consider photons generated in a galaxy cluster or in the jet of a blazar -crossing several magnetized media (blazar jet, host galaxy, galaxy cluster, extragalactic space, Milky Way) up to their arrival at the Earth, where photons can be detected. In the presence of photon-ALP interaction, we analyze the photon survival probability Pγ→γ and the corresponding photon degree of linear polarization ΠL for observed energies in the range (1 − 10 15 ) eV dividing it into three energy bands: (i) X-ray band (10 −3 keV − 10 2 keV), (ii) high-energy (HE) band (10 −1 MeV − 10 4 MeV), (iii) VHE band (10 −2 TeV − 10 3 TeV). We observe that photons, which are expected as unpolarized in the absence of ALPs, are made partially polarized by photon-ALP interaction, which generally modifies the initial photon degree of linear polarization ΠL,0 in a sizable and measurable way. Our findings about the X-ray and HE bands can be tested by current and planned observatories like IXPE, Polstar, COSI, e-ASTROGAM and AMEGO. A possible detection of a departure of the photon polarization from the standard expectations would represent an additional hint for the existence of an ALP. We also discover a peculiar feature in the VHE band, where photons at energies above ∼ 1 TeV are fully polarized because of photon-ALP interaction. A possible detection of this feature would represent a proof for the existence of an ALP, but, unfortunately, current technologies do not allow yet to detect photon polarization up to so high energies.