A measurement of the tensor polarizability of the $2 ^{1}P_{1}$ state of atomic helium has been made by the electric-field level-crossing technique using an atomic-beam apparatus. The experimental procedure is as follows: An atomic beam containing metastable $2 ^{1}S_{0}$ and $2 ^{3}S_{1}$ helium atoms is produced by electron bombardment of ground-state helium atoms. The beam then passes through a region in which the atoms are subjected to a uniform, variable electric field. In this region the $2 ^{1}S_{0}$ atoms are excited to the $2 ^{1}P_{1}$ state by linearly polarized 20 582-\AA{} ($2 ^{1}S_{0}\ensuremath{-}2 ^{1}P_{1}$) resonance radiation. The extreme uv photons emitted in the direction of the incident resonance light when the $2 ^{1}P_{1}$ state decays to the ground state are counted. The sum intensity of the 584-\AA{} ($2 ^{1}P_{1}\ensuremath{-}1 ^{1}S_{0}$) photons and the 601-\AA{} ($2 ^{1}S_{0}\ensuremath{-}1 ^{1}S_{0}$) photons, due to the electric-field quenching of the $2 ^{1}S_{0}$ atoms, is measured as a function of the applied electric field for the incident light polarized at 45\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} to the direction of the static electric field. From these measurements the tensor polarizability ${\ensuremath{\alpha}}_{2}(2 ^{1}P_{1})$ of the $2 ^{1}P_{1}$ state is found to be (3.32 \ifmmode\pm\else\textpm\fi{} 0.10) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}23}$ ${\mathrm{cm}}^{3}$, in good agreement with the theoretically calculated value of 3.34 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}23}$ ${\mathrm{cm}}^{3}$.