  We propose the leading couplings, in an alpha' expansion, of noncommutative
D-branes to RR potentials in a constant NSNS B-field for an arbitrary choice of
noncommutative parameter. The proposal is motivated by some string amplitude
computations. The zero momentum couplings are topological in nature and involve
Elliott's noncommutative Chern character. The finite momentum couplings are
given by smearing the zero momentum operators along an open Wilson line.
Comparisons between the RR couplings in different descriptions lead to a better
understanding of the field redefinitions between gauge field variables (the
Seiberg-Witten map) and help constrain alpha' corrections. In particular we
recover the Seiberg-Witten map conjectured by one of the authors in
hep-th/0011125. We also discuss the dynamics of the transverse scalar fields
and find evidence for a new derivative-driven dielectric effect.
