The polarizations of the (\Upsilon)(1S), (\Upsilon)(2S), and (\Upsilon)(3S) mesons are measured as a function of the charged particle multiplicity in proton-proton collisions at(\sqrt{s}) = 7 TeV. The measurements are performed with a dimuon data sample collected in 2011 by the CMS experiment, corresponding to an integrated luminosity of 4.9 fb⁻¹. The results are extracted from the dimuon decay angular distributions, in two ranges of (\Upsilon)(nS) transverse momentum (10-15 and 15-35 GeV), and in the rapidity interval |y| < 1.2. The results do not show significant changes from low- to high-multiplicity pp collisions, although large uncertainties preclude definite statements in the (\Upsilon)(2S) and (\Upsilon)(3S) cases.