We report a measurement of the differential cross section dσ/d(cosθ(t)) for top-quark pair production as a function of the top-quark production angle in proton-antiproton collisions at sqrt[s] = 1.96 TeV. This measurement is performed using data collected with the CDF II detector at the Tevatron, corresponding to an integrated luminosity of 9.4 fb(-1). We employ the Legendre polynomials to characterize the shape of the differential cross section at the parton level. The observed Legendre coefficients are in good agreement with the prediction of the next-to-leading-order standard-model calculation, with the exception of an excess linear-term coefficient a(1) = 0.40 ± 0.12, compared to the standard-model prediction of a(1)=0.15(-0.03)(+0.07).