  We determine the magnetization of Quantum Chromodynamics (QCD) for several
temperatures around and above the transition between the hadronic and the
quark-gluon phases of strongly interacting matter. We obtain a paramagnetic
response that increases in strength with the temperature. We argue that due to
this paramagnetism, chunks of quark-gluon plasma produced in non-central heavy
ion collisions should become elongated along the direction of the magnetic
field. This anisotropy will then contribute to the elliptic flow v_2 observed
in such collisions, in addition to the pressure gradient that is usually taken
into account. We present a simple estimate for the magnitude of this new effect
and a rough comparison to the effect due to the initial collision geometry. We
conclude that the paramagnetic effect might have a significant impact on the
value of v_2.
