  The conformal symmetry of the quantized electromagnetic field breaks down in
curved space-time. We point out that this conformal anomaly is able to generate
a sizable magnetic field during a phase of slow-roll inflation. Such primordial
magnetism is characterized by the expectation value of the squared of the
magnetic field for comoving observers, which at leading order in slow-roll
takes the value $\ < \vec B^2\ > =\frac{8}{15(4\pi)^2}\, H^4\epsilon$, where
$\epsilon$ is the standard slow-roll parameter. This result is insensitive to
the intrinsic ambiguities of renormalization in curved space-times. The
information in the quantum state gets diluted during inflation and does not
affect the prediction. A primordial field of this strength is able to seed the
observed cosmic magnetism.
