  We study the Quantum Regge Calculus of Einstein-Cartan theory to describe
quantum dynamics of Euclidean space-time discretized as a 4-simplices complex.
Tetrad field e_\mu(x) and spin-connection field \omega_\mu(x) are assigned to
each 1-simplex. Applying the torsion-free Cartan structure equation to each
2-simplex, we discuss parallel transports and construct a diffeomorphism and
{\it local} gauge-invariant Einstein-Cartan action. Invariant holonomies of
tetrad and spin-connection fields along large loops are also given.
Quantization is defined by a bounded partition function with the measure of
SO(4)-group valued \omega_\mu(x) fields and Dirac-matrix valued e_\mu(x) fields
over 4-simplices complex.
