A measurement of the correlations between the polar angles of leptons from the decay of pair-produced t and t¯ quarks in the helicity basis is reported, using proton-proton collision data collected by the ATLAS detector at the LHC. The dataset corresponds to an integrated luminosity of 4.6 fb-1 at a center-of-mass energy of s=7 TeV collected during 2011. Candidate events are selected in the dilepton topology with large missing transverse momentum and at least two jets. The angles θ1 and θ2 between the charged leptons and the direction of motion of the parent quarks in the tt¯ rest frame are sensitive to the spin information, and the distribution of cosθ1·cosθ2 is sensitive to the spin correlation between the t and t¯ quarks. The distribution is unfolded to parton level and compared to the next-to-leading order prediction. A good agreement is observed.