We write down couplings of the fields on a single BPS Dp-brane with noncomm
utative world-volume coordinates to the RR-forms in type-II theories, in a
manifestly background independent way. This generalises the usual Chern-Sim
ons action for a commutative Dp-brane. We show that the noncommutative Cher
n-Simons terms can be mapped to Myers terms on a collection of infinitely m
any D-instantons. We also propose Chern-Simons couplings for unstable non-B
PS branes, and show that condensation of noncommutative tachyons on these b
ranes leads to the correct Myers terms on the decay products.