  We compute the thermo-magnetic correction to the quark-gluon vertex in the
presence of a weak magnetic field within the Hard Thermal Loop approximation.
The vertex satisfies a QED-like Ward identity with the quark self-energy. The
only vertex components that get modified are the longitudinal ones. The
calculation provides a first principles result for the quark anomalous magnetic
moment at high temperature in a weak magnetic field. We extract the effective
thermo-magnetic quark-gluon coupling and show that this decreases as a function
of the field strength. The result supports the idea that the properties of the
effective quark-gluon coupling in the presence of a magnetic field are an
important ingredient to understand the inverse magnetic catalysis phenomenon.
