Although it is not a commonly held belief but some scientists and researchers have hypothesized that due to the shifting of mass of more land and ocean currents towards specific areas, a minor change could take place in the current position of Earth's axis. According to Felix Landerer, the Earth's axis is already tilting by 2.6 centimetres each year because of melting of ice. This number could increase in the coming years.

Other than that, global warming also causes Earth's mass to shift more towards higher attitudes. This causes the Earth to spin faster as the mass is relocated closer to the Earth's spin axis.

Yes,change in climate can cause change in Earth's spin. As due to strong winds the rotation of earth get slower comparative to normal. And which result in increasing the day by just fraction of seconds. Changes in atmospheric pressure around the world can strongly affect the earth’s rotation. There is one law of conservation of angular momentum through which small but detectable changes are found.

The Earth is an oblate spheroid, squashed from pole to pole. The circumference of the earth is 43 Km greater at the equator, as opposed to pole to pole. There are a series of cycles of weather related changes in the earth's rotation, most clearly seen in El Nino; a very short term change. It has been postulated that a 43,000 year cycle has been responsible for ice ages, with the "little" and last ice age being a subset of that. That is but one of many theories; all involve the inclination of the earth to the sun, the overall rate of speed of the earth's annual cycle, and several other arcane effects. During COP15, the Russians postulated that the ice caps were melting due to a slowing of the earth rotation, thus pitching the orb so that more sunlight fell upon the poles; thus climate change has nothing to do with the activity of man, the whole debate thus a hoax. Not very convincing argument, and mostly dismissed out of hand by most scientists. My opinion is based on a simple proposition; as the global ice melts and oceans rise (unequally distributed as that rise may be), one might consider an ice skater performing a spin. By holding out the arms, the rate of spin is increased. The very shape of the earth will change, the poles may tilt or even move, the equator may shift; but by whatever way one looks at the situation, the spin will speed up.