  We consider Very Special Relativity corrections to the energy spectrum of a
$C-$invariant Dirac Fermion in a static and homogeneous magnetic field $\vec
B$. First, in the case of $\vec B$ parallel to the spatial VSR preferred
direction $\vec n$, finding that the expression for the energy spectrum stays
the same, except for a correction to the mass arising from the VSR
contribution. Then, we relax the parallelism condition, finding a new equation
for the energy spectrum. We solve this equation perturbatively. With a Penning
trap's experiment in mind, we derive the first order VSR corrections to the
electron's $g-2$ factor. Finally, using the current errors on the electron's
$g$-factor measurements in Penning trap's experiments, we obtain an upper bound
to the VSR electron mass parameter, and therefore also to the VSR electronic
neutrino mass, of $0.824 \, eV$. This result does not contradict the
possibility for VSR to be the origin of neutrino masses.
