Spin-momentum locking in altermagnets has been deeply explored in the non-relativistic limit. Including spin-orbit coupling, altermagnets exhibit antisymmetric exchange interactions, leading to spin cantings. Therefore, the spin-momentum locking differs among the three spin components Sx, Sy, and Sz, forming the relativistic spin-momentum locking. We consider orthorhombic YVO3 and hexagonal MnTe. For YVO3, the relativistic locking comprises s-, dxy -, and dxz-wave. In MnTe, the dominant component Sy of MnTe inherits the polarized charge distribution and the non-relativistic spin-momentum locking bulk g-wave, but the breaking of the C6z rotational symmetry by the Neel vector lowers the symmetry from g-wave to d-wave. The relativistic spin-momentum locking for MnTe is composed of dxz-, dyz- and s-wave. Despite small magnitudes in real space, the canted spin components contribute significant spectral weight in k-space, impacting k-space properties such as the spin-Hall conductivity.