  We show that the scale (conformal) anomaly in field theories leads to new
anomalous transport effects that emerge in an external electromagnetic field in
an inhomogeneous gravitational background. In inflating geometry the QED scale
anomaly locally generates an electric current that flows in opposite direction
with respect to background electric field (the scale electric effect). In a
static spatially inhomogeneous gravitational background the dissipationless
electric current flows transversely both to the magnetic field axis and to the
gradient of the inhomogeneity (the scale magnetic effect). The anomalous
currents are proportional to the beta function of the theory.
