What effect does climate change have on the Earth's rotation?
The only answer I can come up with is related to isostasy.
1 - Poles melt, so there's more water in the oceans.
2 - As there's more water in the oceans, there's more weight on the oceanic crusts, so they bend, making deeper some parts of the oceans.
3 - The parts of the ocean that are deeper are in the centre of the oceans, far from continental crust. It should be mainly the Pacific Ocean, Indic and Atlantic, but not near Antarctica, as this area is continental crust (lighter) and will be also unloaded from ice.
4 - As a result, the shape of the Earth crust becomes a bit longer in N-S direction.
5 - As the mass of the Earth is closer to the rotation axis, it accelerates the spin.
Lithospheric density is approximately 2.5 times that of water, so amount of water in the ocean isn't as important as crust flexion.