  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.
