  Motivated by the experimental observation that superconductivity in bulk
doped SrTiO$_{3}$ is enhanced as a putative ferroelectric quantum critical
point (FE-QCP) is approached, we study the pairing instability of a cubic
system in which electrons exchange low-energy ferroelectric fluctuations.
Instead of the gradient coupling to the lattice distortion associated with
ferroelectricity, we consider a direct coupling between the electrons and the
bosonic ferroelectric field that appears in the presence of spin-orbit
coupling. Working in the weak-coupling regime, we find that the pairing
interaction is dominated by the soft transverse optical (TO) mode, resulting in
a $T_{c}$ enhancement upon approaching the FE-QCP. Focusing on even-parity
states, we find that although the $s$-wave state always wins, states with
higher Cooper-pair angular momentum become close competitors as the TO mode
softens. We show that the cubic anisotropy of the FE fluctuations mixes the
$s$-wave and $g$-wave states, resulting in a characteristic anisotropy of the
gap function. The gap anisotropy behaves non-monotonically as the FE-QCP is
approached: upon decreasing the TO mode frequency, the gap anisotropy first
changes sign and then increases in magnitude. We discuss the possible
applications of our results to the superconducting state of SrTiO$_{3}$.
