These particles have half-integer spin, so their angular momentum can't be explained as if they're physical objects spinning rigidly. That would produce only integer values of angular momentum.
They do "really" precess in the following sense. Suppose you prepare an electron in state A, with its spin pointing along the positive x axis. Then you subject it to a magnetic field along the z axis and let it act for an amount of time that would, classically, cause a precession by some angle. For example, let's say it's 90 degrees counterclockwise about the z axis. Now it's in some state B. If you then measure the component of the electron's spin along the y axis, you will find what you expected, with 100% probability: the spin is aligned with the y axis.
But the results of other measurements on B will not give the results you would expect classically. For example, if you measure the component of the spin along the x axis, you will not get zero. (That's not a possible value for a spin-1/2 particle.) You will get either +1/2 or -1/2, with equal probability.
The answer by anna v is wrong. She says, "The (x,y,z) of particles in the quantum mechanical frame are described by orbitals , probability loci where a measurement will give the non-sequential (x,y,z) of a particle." The spin-1/2 of an electron has nothing to do with the x, y, and z degrees of freedom.