  Built upon the proposal of Kaplan et.al. [hep-lat/0206109], we construct
noncommutative lattice gauge theory with manifest supersymmetry. We show that
such theory is naturally implementable via orbifold conditions generalizing
those used by Kaplan {\sl et.al.} We present the prescription in detail and
illustrate it for noncommutative gauge theories latticized partially in two
dimensions. We point out a deformation freedom in the defining theory by a
complex-parameter, reminiscent of discrete torsion in string theory. We show
that, in the continuum limit, the supersymmetry is enhanced only at a
particular value of the deformation parameter, determined solely by the size of
the noncommutativity.
