  A class of stationary rigidly rotating perfect fluid coupled with non-linear
electromagnetic fields was investigated. An exact solution of the Einstein
equations with sources for the Carter B(+) branch was found, for the equation
of state $3p + \epsilon = constant$. We use a structural function for the
Born-Infeld non-linear electrodynamics which is invariant under duality
rotations and a metric possessing a four- parameter group of motions. The
solution is of Petrov type D and the eigenvectors of the electromagnetic field
are aligned to the Debever-Penrose vectors.
