  Low-energy Lorentz-invariant quantities could receive contributions from a
fundamental theory producing small Lorentz-violating effects. Within the
Lorentz-violating extension of quantum electrodynamics, we investigate,
perturbatively, the contributions to the one-loop $ff\gamma$ vertex from the
$CPT$-violating axial coupling of a vector background field to fermions. We
find that the resulting vertex function has a larger set of Lorentz structures
than the one characterizing the usual, Lorentz invariant, parametrization of
the $ff\gamma$ vertex. We prove gauge invariance of the resulting one-loop
expression through a set of gauge invariant nonrenormalizable operators
introducing new-physics effects at the first and second orders in Lorentz
violation, and which generate tree-level contributions to the $ff\gamma$
vertex. Whereas loop contributions involving parameters that violate Lorentz
invariance at the first order are $CPT$-odd, those arising at the second order
are $CPT$-even, so that contributions to low-energy physics are restricted to
emerge for the first time at the second order. In this context, we derive a
contribution to anomalous magnetic moment of fermions, which we use to set a
bound on Lorentz violation.
