Apparently, some people in the Soviet Union thought so, and in the 1970s tried to build a device which would use gyroscopes to drive generators with energy extracted from the Earth’s rotation (it has plenty to spare: the rotational kinetic energy of the Earth is around 2.14\times 10^{29} joules), but they were never able to get it to work.
I don’t see how any mechanism coupled to the rotating Earth could extract energy from its rotation without violating conservation of angular momentum. A scheme such as a generating electricity from tidal water flow does extract energy from the Earth’s rotation, but requires the gravitational action of an external body such as the Moon, whose tidal recession balances the angular momentum extracted from the Earth.