In the present study, we explore the spin alignment of \(\rho \) , \(\phi \) , and \(K^{*0}\) vector mesons assuming the quarks (and anti-quarks) are polarized in the relativistic heavy-ion collisions. The initial orbital angular momentum imparted in the system due to the colliding nuclei helps to polarize the quarks in the medium and these quark-polarization is inherited to the hadron polarization. We explore the effect of external magnetic field eB and medium momentum-space anisotropy \(\xi \) on the spin-alignment of these vector mesons through the diagonal elements of the spin-density matrix \(\rho _{00}\) . We consider two distinct hadronization processes: quark recombination and fragmentation to investigate this effect. Our findings reveal that is inversely related to medium anisotropy and directly related to the strength of the magnetic field, providing a qualitative explanation for the experimental data observed.