Question

how does the earth started rotation

Answer 1

Thinking back to the formation of all the planets, matter--in whatever form, solid, liquid or gas--clumped together by gravity. But the probability that it would do that in a completely uniform way, with equal masses imparting symmetric angular momentum to the earth is zero. In other words, the process was slightly chaotic and asymmetric.

So this is why all planets and moons rotate with respect to the inertial frame of the sun and why none of them have an axis of rotation exactly perpendicular to the plane of their orbit.

Answer 2

the earth started it's rotation when it formed

Answer 3

In a gravity field of positive curl.