We report measurements of the Stark shift of the cesium $6s : ^2S_{3/2} rightarrow 7p : ^2P_{3/2} $ and the $6s : ^2S_{1/2} rightarrow 7p : ^2P_{1/2} $ transitions at $lambda = 456$ 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 $sim$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.
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