While the spin of an electron, etc. cannot be envisioned as the rotation of a rigid body, it is not true that this spin "has nothing to do with" the spinning of a tennis ball. They represent the same conserved quantity, angular momentum.
If you align the spins of photons, for example (i.e. circularly polarized light), and shine the beam at an opaque object, you will impart a measurable torque to it.