  Current experimental data guarantees the presence of physics beyond the
Standard Model in the neutrino sector. The responsible physical description
might show itself through virtual effects on low-energy observables. In
particular, massive neutrinos are able to produce contributions to the triple
gauge coupling $WW\gamma$. The present paper deals with the calculation,
estimation and analysis of one-loop contributions from Majorana neutrinos to
the Lorentz-covariant $WW\gamma$ parametrization. Our calculations show that
CP-odd effects vanish exactly, whereas CP-even contributions, $\Delta\kappa$
and $\Delta Q$, remain. According to our estimations, the effects from heavy
neutrinos with masses in the range of hundreds of GeVs dominate over those from
light neutrinos. This investigation shows that contributions from heavy
Majorana neutrinos to the anomaly $\Delta\kappa$ could be as large as
$\sim{\cal O}(10^{-3})$, one order of magnitude below the Standard-Model
contribution. We find that the International Linear Collider, sensitive to
triple gauge couplings participating in $WW$ production, might measure these
effects in electron-positron collisions at a center-of-mass energy of
$800\,{\rm GeV}$, as long as heavy-neutrino masses are $\gtrsim300\,{\rm GeV}$
and below $\sim1500\,{\rm GeV}$.
