  The Konishi anomalies for noncommutative N=1 supersymmetric U(1) gauge theory
arising from planar and nonplanar diagrams are calculated. Whereas planar
Konishi anomaly is the expected \star-deformation of the commutative anomaly,
nonplanar anomaly reflects the important features of nonplanar diagrams of
noncommutative gauge theories, such as UV/IR mixing and the appearance of
nonlocal open Wilson lines. We use the planar and nonplanar Konishi anomalies
to calculate the effective superpotential of the theory. In the limit of
vanishing |\Theta p|, with \Theta the noncommutativity parameter, the
noncommutative effective superpotential depends on a gauge invariant
superfield, which includes supersymmetric Wilson lines, and has nontrivial
dependence on the gauge field supermultiplet.
