We predict a new effect due to the presence of the global vorticity in non-central relativistic heavy-ion collisions, namely a splitting of the elliptic flow parameter $v_2$ at non-zero rapidity. The size of the splitting is proposed as a new observable that can be used to constrain the initial vortical configuration of the produced QCD matter in experiments. The new findings are demonstrated by numerical calculations employing the parton cascade model, Boltzmann Approach of MultiParton Scatterings (BAMPS), for non-central Au + Au collisions at $sqrt{s_{NN}} = 200 GeV$.