  We present a framework in which the projective symmetry of the
Einstein-Hilbert action in metric-affine gravity is used to induce an effective
coupling between the Dirac lagrangian and the Maxwell field. The effective
$U(1)$ gauge potential arises as the trace of the non-metricity tensor $Q_{\mu
a}{}^a$ and couples in the appropriate way to the Dirac fields to in order to
allow for local phase shifts. On shell, the obtained theory is equivalent to
Einstein-Cartan-Maxwell theory in presence of Dirac spinors.
