Bilayers composed of two ferromagnetic Chern-insulating V2WS4 monolayers coupled antiferromagnetically between the layers have recently been identified as a promising platform for realizing an altermagnetic state characterized by a d-wave spin texture. In this work, we investigate the impact of spin–orbit coupling (SOC) on the altermagnetic spin texture in bilayer V2WS4 using first-principles calculations. In the absence of SOC, our nonrelativistic calculations reproduce a distinct altermagnetic state characterized by a d-wave spin texture, with a strictly vanishing net magnetization and a momentum-dependent altermagnetic spin polarization. Upon inclusion of SOC, however, the characteristic nonrelativistic d-wave spin texture undergoes a continuous SOC-driven reconstruction into a relativistic noncollinear momentum-space spin texture. Our fully relativistic calculations reveal that, although the net magnetization remains exactly zero and the momentum-dependent spin polarization persists owing to the underlying antiunitary symmetries, the spin texture becomes noncollinear with finite Sx and Sy components beyond the nonrelativistic d-wave form. These results demonstrate that, while the symmetry-protected altermagnetic characteristics in bilayer V2WS4 are robust against SOC, the specific nonrelativistic d-wave spin texture is reconstructed by relativistic effects. Our study therefore provides a material-specific first-principles analysis of the SOC-driven reconstruction of the altermagnetic spin texture in bilayer V2WS4 and highlights how relativistic effects modify its electronic and spin structures.