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 the dilepton rest frame 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 cos2phi dependence is found in these proton-induced Drell-Yan data, in contrast with the situation for pion-induced Drell-Yan data. The data are compared with expectations from models which attribute the cos2phi distribution to a QCD vacuum effect or to the presence of the transverse-momentum-dependent Boer-Mulders structure function h{1}{perpendicular}. Constraints on the magnitude of the sea-quark h{1}{perpendicular} structure functions are obtained.