  We introduce the electromagnetic-gravitational coupling in the
Ho\v{r}ava-Lifshitz framework, in $3+1$ dimensions, by considering the
Ho\v{r}ava-Lifshitz gravity theory in $4+1$ dimensions at the kinetic conformal
point and then performing a Kaluza-Klein reduction to $3+1$ dimensions. The
action of the theory is second order in time derivatives and the potential
contains only higher order spacelike derivatives up to $z=4$, $z$ being the
critical exponent. These terms include also higher order derivative terms of
the electromagnetic field. The propagating degrees of freedom of the theory are
exactly the same as in the Einstein-Maxwell theory. We obtain the Hamiltonian,
the field equations and show consistency of the constraint system. The kinetic
conformal point is protected from quantum corrections by a second class
constraint. At low energies the theory depends on two coupling constants,
$\beta$ and $\alpha$. We show that the anisotropic field equations for the
gauge vector is a deviation of the covariant Maxwell equations by a term
depending on $\beta-1$. Consequently, for $\beta=1$, Maxwell equations arise
from the anisotropic theory at low energies. We also prove that the anisotropic
electromagnetic-gravitational theory at the IR point $\beta=1$, $\alpha=0$, is
exactly the Einstein-Maxwell theory in a gravitational gauge used in the ADM
formulation of General Relativity.
