Gapless fracton quantum spin liquids are exotic phases of matter  described by higher-rank generalizations of U(1) quantum electromagnetism which host massive and immobile fracton matter excitations as well as gapless photons. Despite well-known field theories, no spin models beyond purely classical systems have been proposed to realize these phases. After revisiting a simple but instructive example of how U(1) electrodynamics can emerge in a spin system, we apply this knowledge to introduce a square lattice spin model that shows precise signatures of classical and quantum fracton spin liquids depending on the spin quantum number. Using Green Function Monte Carlo, we will see that the ground state of the sign-problem free spin-1 quantum version shows no indications of conventional ordering and accurately matches the prediction of a rank-2 U(1) field theory onto which this model can be mapped, providing compelling evidence for a fracton quantum spin liquid with emergent photon excitations.