  A Kerr type solution in the Regge calculus is considered. It is assumed that
the discrete general relativity, the Regge calculus, is quantized within the
path integral approach. The only consequence of this approach used here is the
existence of a length scale at which edge lengths are loosely fixed, as
considered in our earlier paper.
  In addition, we previously considered the Regge action on a simplicial
manifold on which the vertices are coordinatized and the corresponding
piecewise constant metric introduced, and found that for the simplest periodic
simplicial structure and in the leading order over metric variations between
4-simplices, this reduces to a finite-difference form of the Hilbert-Einstein
action.
  The problem of solving the corresponding discrete Einstein equations
(classical) with a length scale (having a quantum nature) arises as the problem
of determining the optimal background metric for the perturbative expansion
generated by the functional integral. Using an one-complex-function ansatz for
the metric, which reduces to the Kerr-Schild metric in the continuum, we find a
discrete metric that approximates the continuum one at large distances and is
nonsingular on the (earlier) singularity ring. The effective curvature
$R_{\lambda \nu \nu \rho }$, including where $R_{\lambda \mu} \neq 0$ (gravity
sources), is analyzed with a focus on the vicinity of the singularity ring.
