  We present a noncommutative extension of Einstein-Hilbert gravity in the
context of twist-deformed space-time, with a $\star$-product associated to a
quite general triangular Drinfeld twist. In particular the $\star$-product can
be chosen to be the usual Groenewald-Moyal product. The action is geometric,
invariant under diffeomorphisms and centrally extended Lorentz $\star$-gauge
transformations. In the commutative limit it reduces to ordinary gravity, with
local Lorentz invariance and usual real vielbein. This we achieve by imposing a
charge conjugation condition on the noncommutative vielbein. The theory is
coupled to fermions, by adding the analog of the Dirac action in curved space.
A noncommutative Majorana condition can be imposed, consistent with the
$\star$-gauge transformations. Finally, we discuss the noncommutative version
of the Mac-Dowell Mansouri action, quadratic in curvatures.
