The Faraday effect is dispersive, so it is coherent and reversible. It tweaks the evolution of the light but doesn't cause "relaxation". In general, a system cannot reach a ground state, like becoming aligned to a magnetic field, without some sort of dissipation (e.g., absorption).
The linear algebra way to think about this is as follows: consider orthogonal states of light, such as $H$ and $V$ linear polarizations. After coherent evolution, they remain orthogonal, or else the evolution would not be reversible (given the final state, the initial state can be uniquely determined). This logic shows us the range of possible options for coherent evolution. The polarization can rotate (like the Faraday effect), it can go from linear to elliptical or circular (like a quarter waveplate), or it can undergo a mirror reflection (like a half waveplate). Of course, any combination of those options is also valid. But it can't align without ''losing information'', which would require a absorptive polarizer. (What I've just described is the $U(2)$ group of unitary matrices on $2\times 2$ complex vectors.)
Note: when I say "reversible", I mean coherent or unitary. I'm not referring to time reversal symmetry, which the Faraday effect breaks.
Edit If we're looking for a way for light to align to the magnetic field, we need the information on the original polarization of the light to be lost. The Faraday effect is off-resonant and cannot achieve that. One way to realize this is through dichroism, where one polarization (usually circular) of light is absorbed. This process is clearly not coherent/unitary because it erases the information on what the incoming polarization is. After absorption, with the right setup, the light can become aligned with the magnetic field. (I can give an explicit example with atoms, if you'd like.)
Sorry if this repeats my comment.