Producing Ba+ ions by laser ablation of a BaTiO3 chip and detecting their laser induced fluorescences, the cross section for the collision induced transition between fine structure levels in the 6p (2)p(J) state due to collisions with He atoms at room temperature (298 K) has been measured. The cross section thus determined is sigma(6p P-2(3/2) -> 6p P-2(1/2)) = (2.93 +/- 0.37) x 10(-4) angstrom(2).