We performed first-principles calculations of the spin-orbit effect appearing in the electronic structure of the well-known ferroelectric perovskite oxide PbTiO3 and analyzed the results within group-theory-derived models. We evidenced some non-negligible linear Rasbha spin splittings of the unoccupied p bands of Pb atoms and occupied p bands of oxygen atoms. Our calculations also show that a cubic spin splitting is present for the unoccupied dxy bands of Ti atoms. All these spin-orbit effects lead to complex spin textures reversible by switching the electric polarization, which could be used for future spinorbitronic applications. Our results also demonstrate how applying epitaxial strain could be envisaged to tune these properties by changing the relative energy of some of the bands or the magnitude of the linear/cubic coefficients describing the spin splitting.