Is there a way to relate gravity with magnetism through a universal law?

Electromagnetism is just a low energy manifistation of a quantum mechanical effect called the nuclear electroweak force. Unifying it and another quantum effect (strong force), and those in turn with gravity are principle preoccupations of theoretical particle physicists. Google "Superforce", "String Theory" and "Supergravity" approaches. It has been quite ellusive. The main problem is that in order to experimentally observe the relationship between the forces, one needs to be in a regime where both gravity and quantum mechanics have comparable effects. Called the "Planck Scale" (Google), this requires particle energies vastly greater than anything that can be created or observed. It's a regime the universe went through very early on (sub nanoseconds after Big Bang), so understanding it means understand the BB's cause.