The competition between the Zeeman energy and the Rashba and Dresselhaus spin-orbit couplings is studied for ferromagnetic states in the fractional quantum Hall regime. A transition of the spin-polarization direction, which acquires an in-plane component even if the magnetic field is perpendicular to the quantum well, is predicted to occur at small values of the Zeeman energy, as an effect of the spin-orbit interaction. For a given fractional state, we theoretically investigate this phenomenon in the perturbative limit of high magnetic fields. We consider the Laughlin wave functions and the Pfaffian state as specific examples of possible ground states, and show that the quantitative features of this transition provide valuable information about the nature of the correlated ground-state. In particular, a relation to the pair-correlation function is derived. We also discuss indications of non-analytic features around the fractional states and include effects of the nuclear bath polarization, which are significant in a relevant range of temperatures and magnetic fields.