What is the moment of inertia of a free electron?

Well, elementary particles have no moment of inertia $I$. But what is the nearest possible answer to the question for a free, spinning electron?

In general, one has a relation with spin $J$ given by
$$ J = I omega.$$
For an electron, the magnitude of spin is $J=sqrt{3/4} hbar$. But since $omega$ is not defined, there is no way to speak about a moment of inertia.

Or can one say more?