We report a measurement of the angular distributions of Drell-Yan dimuons produced using an 800 GeV/c proton beam on a deuterium target. The muon angular distributions in polar angle \(\theta\) and azimuthal angle \(\phi\) have been measured over the kinematic range \(4.5 < m_{\mu \mu} < 15\) GeV/c\(^2\), \(0 < p_T < 4 \) GeV/c, and \(0 < x_F < 0.8\). No significant cos\(2\phi\) dependence is found in these proton-induced Drell-Yan data, in contrast to the situation for pion-induced Drell-Yan. The data are compared with expectations from models which attribute the cos\(2\phi\) distribution to a QCD vacuum effect or to the presence of the transverse-momentum-dependent Boer-Mulders structure function \(h_1^\perp\). Constraints on the magnitude of the sea-quark \(h_1^\perp\) structure functions are obtained.