  In this work we calculate the pole-mass of the $\rho^0$ meson with different
spin projections $s_z=0,\pm 1$ in the context of the magnetized two-flavor
Nambu--Jona--Lasinio model. Making use of the mean field approximation to
obtain the effective quark mass as a function of the magnetic field, we apply
the random phase approximation (RPA) to the vector channel in order to
calculate the polarization function for each spin component. We adopt the
magnetic field independent regularization (MFIR) in our evaluations as a method
of separating divergences and the Pauli-Villars regularization for the vacuum
contributions. The $\rho^0$ meson mass with spin projection $s_z=\pm 1$ is
always catalysed with the magnitude of the magnetic field, showing good
agreement with Lattice QCD results. The mass projection $s_z=0$ has a
non-monotonic behavior, decreasing until the minimum at $eB\lesssim 0.15$
GeV$^2$, which is in contrast with available LQCD data.
