It actually can't be rotation, otherwise the magnetic moment of charged particles comes out wrong by a factor two. From the mathematicians point of view spin a

It actually can't be rotation, otherwise the magnetic moment of charged particles comes out wrong by a factor two. From the mathematicians point of view spin arises naturally when you study how to represent the symmetries of special relativity. Quantum mechanics taught us that a physical state is represented by something called the "wave function". Different observers (e.g. one moving relatively to the other with constant speed) see different "wave functions" representing the same state. Studying all mathematically consistent possibilities of how to calculate what one observer sees if you know what the other sees leads to the possibility of particles with spin.