Just as waves spread out when a boat moves in water or a stone is thrown in a pond, gravitational waves are distortions in the curvature of space-time caused by motions of matter that propagate with the speed of light.
It turns out that one type of gluon chain behaves in the four-dimensional spacetime as the graviton, the fundamental quantum particle of gravity. In this description, gravity in four dimensions is an emergent phenomenon arising from particle interactions in a gravityless, three-dimensional world.
Since matter carries energy, such objects will have a gravitational field and so they will distort space-time. So one way in which a charge or a magnet will distort space-time is by virtue of its matter.
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