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A discrete theory of gravity locally invariant under the Poincar\'e group isconsidered as in a companion paper. We define a first order theory, in thesense of Palatini, on the metric-dual Voronoi complex of a simplicial complex.We follow the same spirit of the continuum theory of General Relativity in theCartan formalism. The field equations are carefully derived taking in accountthe constraints of the theory. They look very similar to first order Einsteinequations in the Cartan formalism. It is shown that in the limit of {\it smalldeficit angles} these equations have Regge Calculus, locally, as the onlysolution. A quantum measure is easly defined which does not suffer theambiguities of Regge Calculus, and a coupling with fermionic matter is easilyintroducedComment: Revised version, 18 pages, 2 figures, accepted by Classical and  Quantum Gravit

Discrete gravity as a local theory of the Poincaré group in the first-order formalism