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The only scientific evidence I can find the Earth is spinning is Foucault's Pendulum but that can be accounted for in a geocentric model: 

"If one rotates the shell relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell, that is, the plane of a Foucault pendulum is dragged around" - Albert Einstein, cited in "Gravitation", Misner Thorne and Wheeler pp. 544-545. 

"...Thus we may return to Ptolemy's point of view of a 'motionless earth'...One has to show that the transformed metric can be regarded as produced according to Einstein's field equations, by distant rotating masses. This has been done by Thirring. He calculated a field due to a rotating, hollow, thick-walled sphere and proved that inside the cavity it behaved as though there were centrifugal and other inertial forces usually attributed to absolute space. Thus from Einstein's point of view, Ptolemy and Corpenicus are equally right." - Max Born, "Einstein's Theory of Relativity", Dover Publications, 1962, pp 344 & 345. 

A June 25, 1913 letter from Einstein to Ernst Mach* concerning such forces from a relativistic point of view: 

"[Y]our happy investigations on the foundations of mechanics, Planck's unjustified criticism notwithstanding, will receive brilliant confirmation. For it necessarily turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton's pail experiment. The first consequence is on p. 6 of my paper. The following additional points emerge:*(1) If one accelerates a heavy shell of matter S, then a mass enclosed by that shell experiences an accelerative force. (2) If one rotates the shell relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell, that is, the plane of a Foucault pendulum is dragged around.

*In the Ptolemaic system, the earth is considered to be at rest and without rotation in the center of the universe, while the sun, other planets and fixed stars rotate around the earth. In relational mechanics this rotation of distant matter yields the force ... Now the gravitational attraction of the sun is balanced by a real gravitational centrifugal force due to the annual rotation of distant masses around the earth (with a component having a period of one year). In this way the earth can remain at rest and at an essentially constant distance from the sun. The diurnal rotation of distant masses around the earth (with a period of one day) yields a real gravitational centrifugal force flattening the earth at the poles. Foucault’s pendulum is explained by a real Coriolis force acting on moving masses over the earth’s surface ...The effect of this force will be to keep the plane of oscillation of the pendulum rotating together with the fixed stars. 

- Andre K. T. Assis, professor of physics at the University of Campinas - UNICAMP, in Brazil) Relational Mechanics, pp. 190-191