Optical activity of electromagnetic waves in a string inspired Kalb–Ramond cosmological background is studied in the presence of an extra spacetime dimension. The Kalb–Ramond-electromagnetic coupling, which originates from the gauge anomaly cancelling Chern–Simons term in a string inspired model, is explicitly calculated following the Randall–Sundrum braneworld conjecture. It is shown that the Randall–Sundrum scenario leads to an enormous enhancement of the optical rotation of a plane polarized electromagnetic wave propagating on the visible brane. The absence of any experimental support in favour of such a large rotation in astrophysical experiments on distant galactic radio waves indicates an apparent conflict between the Randall–Sundrum braneworld scenario and the presence of the Kalb–Ramond antisymmetric tensor field in the background spacetime.