  We present a covariant canonical formalism for noncommutative gravity, and in
general for noncommutative geometric theories defined via a twisted
$\star$-wedge product between forms. Noether theorems are generalized to the
noncommutative setting, and gauge generators are constructed in a twisted phase
space with $\star$-deformed Poisson bracket. This formalism is applied to
noncommutative $d=4$ vierbein gravity, and allows to find the canonical
generators of the tangent space $\star$-gauge group.
