We examine the relationship between the masslessness of a photon and symmetry realizations in (2 + 1)-dimensional scalar QED. We find that this masslessness is a direct consequence of spontaneous breaking of a global symmetry, whose generator is the magnetic flux. The pertinent order parameter for the Higgs-Coulomb phase transition is identified with the VEV of the magnetic vortex creation operator V(x). We calculate, using weak coupling perturbation theory, the VEV and the correlator of V(x) in both phases. This turns out to be equivalent to evaluating the Euclidean QED partition function in the presence of the external current which produces a magnetic monopole (with the contribution of the Dirac string subtracted). In the Coulomb phase is finite, while in the Higgs phase it vanishes.