Is the atmosphere of the Earth thicker at the equator due to rotation?

Yes it is. I don't have the precise values but at the poles, any gas located there is in equilibrium with just the gravitational field of the Earth, while at the equator, the rotation of the Earth provides a slight diminution of the force of gravity ( you weigh less at the equator than at the pole...try this the next time you are in Hawaii!) gas at the same temperature as at the poles is at pressure equilibrium at a slightly greater distance from the Earth's surface. This effect is probably masked by the fact that the cooler gas at the poles sinks to a lower altitude than the warmer tropical gas. In other words, the scale height for the atmosphere at the equator is larger than at the poles due to thermal effects alone. But in principle, the atmosphere should extend further out at the equator. Perhaps some expert in atmospheric physics who reads this could comment?