It has been recently suggested that the coexistence of ferroelectricity and Rashba-like spin-splitting effects due to spin-orbit coupling in a single material may allow for a non-volatile electric control of spin degrees of freedom. In the present work, we compared the structural and ferroelectric properties of tetragonal and rhombohedral phases of ferroelectric BiAlO3 by means of densityfunctional calculations. In both phases, we carefully investigated Rashba and Dresselhaus effects, giving rise to spin-splitting in their bulk electronic structure, particularly near the conduction band minimum, supplementing our first-principles results with an effective k · p model analysis. The full reversal of the spin texture with ferroelectric polarization switching was also predicted. BiAlO3 can therefore be considered as the first known oxide to exhibit a coexistence of ferroelectricity and Rashba-Dresselhaus effects.