  The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in
terms of spinor notations. In this paper, we consider a noncommutative space
with the Poisson structure and construct an SL(2,C) formulation of gravity on
such a space. Using the covariant coordinate technique, we build a gauge
invariant action in which, according to the Seiberg-Witten map, the physical
degrees of freedom are expressed in terms of their commutative counterparts up
to the first order in noncommutative parameters.
