Abstract : Quarkonium hadroproduction is a long standing puzzle which tests the ability of particle physicists to describe colour interactions. Even if the structure of quantum chromodynamics (QCD) is well established and inspired to quantum electrodynamics (QED), its differences with respect to the latter make the theoretical description of hadron properties very difficult.Many models and effective field theories have been proposed in order to describe heavy quarkonia production, but none of them have been able to predict different observables in a reliable way. In particular, nonrelativistic QCD (NRQCD) succeeded in describing quarkonia cross sections at the Tevatron, but failed in predicting the degree of polarization of the J/psi. On the other hand, the color-singlet model (CSM) had slightly better results from the polarization side, but had problems with the magnitude and differential shapes of the cross sections.The startup of the LHC at CERN provides a very important experimental opportunity in solving these problems. Indeed, the big jump in energy with respect to Tevatron leads to much higher heavy-quarks cross sections than in the past and, moreover, the very good performances of the LHC experiments allow to perform delicate analysis.ALICE is the LHC experiment dedicated to the study of the dense and hot matter produce in ultrarelativistic heavy ions collisions: the quark gluon plasma (QGP). During the first two years of data taking it showed very good performance in the detection of J/psi, both in PbPb and pp collisions.In this thesis, the polarization measurement of J/psi inclusively produced in pp collisions at a center of mass energy of 7 TeV is presented. The analysis was performed on almost 80% of the statistics collected by the ALICE forward muon spectrometer during 2010. It was based on the extraction of the angular distribution of the muons coming from the J/psi decay. The results obtained with this study represent the first measurement of quarkonia polarization at the LHC and they offer the possibility to test the theoretical models in a more than three times higher energy regime with respect to Tevatron. A first comparison with recent theoretical calculations is also presented in this document.