Is there a strong galactic magnetic field?
No, the galactic magnetic field is very weak, about 0.1nT.
It is able to bend the trajectory of highly-energetic charged particles and also to align dust grains across the magnetic field.

However, is too weak to affect the rotation of a galaxy.

Although the origin of galactic magnetic field is not clear yet, the supermassive black holes do not significantly influence the galactic magnetic field far from them.