The scattering of a straight, infinitely long string by a rotating black hole is considered. We assume that a string is moving with velocity v and that initially the string is parallel to the axis of rotation of the black hole. We demonstrate that as a result of scattering, the string is displaced in the direction perpendicular to the velocity by an amount κ(v, b), where b is the impact parameter. The late-time solution is represented by a kink and anti-kink, propagating in opposite directions at the speed of light, and leaving behind them the string in a new phase. We present the results of the numerical study of the string scattering and their comparison with the weak-field approximation, valid where the impact parameter is large, b/M ≫ 1, and also with the scattering by a non-rotating black hole which was studied in earlier works.