The branes that source the RR fields of supergravity are described by the DBI action plus a CS term. I know this only from superstring considerations.
Is there a way to find this result without requiring superstring arguments?
It should, but I am not sure. I would say that one consider deformations of a static, flat brane, and asking for the deformation to be again solution of sugra equations would impose conditions on the deformations, themselves equivalent to equations of motion derived from the brane action, but I am not sure. Does someone have seen something like this in the literature?