  A parent action is introduced to formulate (S-) dual of non-anticommutative
N=1\2 supersymmetric U(1) gauge theory. Partition function for parent action in
phase space is utilized to establish the equivalence of partition functions of
the theories which this parent action produces. Thus, duality invariance of
non-anticommutative N=1\2 supersymmetric U(1) gauge theory follows. The results
which we obtained are valid at tree level or equivalently at the first order in
the nonanticommutativity parameter C_{\mu\nu}.
