  We study theoretically the renormalization of the spin-orbit coupling
constant of two-dimensional electrons by electron-electron interactions. We
demonstrate that, similarly to the $g$ factor, the renormalization corresponds
to the enhancement, although the magnitude of the enhancement is weaker than
that for the $g$ factor. For high electron concentrations (small interaction
parameter $r_s$) the enhancement factor is evaluated analytically within the
static random phase approximation. For large $r_s\sim 10$ we use an approximate
expression for effective electron-electron interaction, which takes into
account the local field factor, and calculate the enhancement numerically. We
also study the interplay between the interaction-enhanced Zeeman splitting and
interaction-enhanced spin-orbit coupling.
