We propose a three-dimensional directional cloak for arbitrarily polarized incoming electromagnetic waves, motivated by the fact that there will be negligible scattering when the direction of impinging wave coincides with the axial direction of a very thin and elongated perfectly electric conducting (PEC) scatterer. The performance of the cloak under different polarizations of incoming waves are numerically investigated. The case in which the direction of incoming wave is perturbed off the ideal direction is also quantitatively studied. Numerical simulations show that the directional cloaking device is able to tolerate a large range of tilted angles of incoming waves.