Interestingly, that wouldn't be physically possible.

The process of accretion in zero gee creates angular momentum by its nature: stuff slams into other stuff and that kinetic energy has to go somewhere, and it can't go any further towards or back away from the centre of gravity... so it goes sideways and turns into a spin.

That's why neutron stars generally rotate near the speed of light; all that matter came inwards with the force of a supernova, so supercharged the spin. Also why black holes spin and accretion disk form. You basically can't have a body of matter coalesce in space without it starting to spin at least a bit. Well, unless you're physically there to carefully place the matter bit by bit with near zero kinetic force, anyway.

If we had no moon then there would be no signficant drag (though there would still be a tiny, tiny, tiny bit from the sun and other bodies in the solar system, but barely noticeable even in astronomical timescales), and we would for all intent and purposes basically never stop or slow our spinning.