We report measurements of the Stark shift of the cesium 6s 2 S 3/2 → 7p 2 P 3/2 and the 6s 2 S 1/2 → 7p 2 P 1/2 transitions at λ = 456 nm and 459 nm, respectively, in an atomic beam. From these, we determine the static scalar polarizability for both 7P states, and the tensor polarizability for the 7P 3/2 state. The fractional uncertainty of the scalar polarizabilites is ∼0.18%, while that of the tensor term is 0.66%. These measurements provide sensitive tests of theoretical models of the Cs atom, which has played a central role in parity nonconservation measurements.