Answer
Earth's angular velocity $\omega$ will decrease.
Work Step by Step
According to the conservation of angular momentum, $$ I_0\omega_0=I_f\omega_f$$
When the ice cap at the South Pole, where the Earth's axis of rotation passes, melts, the mass from the ice cap is distributed evenly in the oceans. That means the distance $R$ of the former ice cap's mass from the axis of rotation increases. And because $I=\sum MR^2$, Earth's moment of inertia increases, too.
Because angular momentum is conserved before and after the action, since $I$ increases, Earth's angular velocity $\omega$ will decrease.
