We present a measurement of the polar-angle distribution of leptons from W boson decay, as a function of the W transverse momentum. The measurement uses an 80±4pb-1 sample of pp¯ collisions at s√=1.8TeV collected by the CDF detector and includes data from both the W⃗ e+ν and W⃗ μ+ν decay channels. We fit the W boson transverse mass distribution to a set of templates from a Monte Carlo event generator and detector simulation in several ranges of the W transverse momentum. The measurement agrees with the standard model expectation, whereby the ratio of longitudinally to transversely polarized W bosons, in the Collins-Soper W rest frame, increases with the W transverse momentum at a rate of approximately 15% per 10GeV/c.