Your question is somewhat ill-defined, as "the fabric of spacetime" is a poetic term. However, the modern theory of gravity is general relativity, which says that 'gravity' and the 'shape of space(time)' are the same thing.
To get some idea of how the above might be true, imagine two people standing on the equator, facing north. If they both walk forward as straight as possible, then although they begin parallel, they will get closer and closer together, and eventually collide at the north pole. If they did not know about the curvature of the Earth, they might conclude that some mysterious force attracted them to each other as they walked north. In the case of spacetime, this 'mysterious force' is what we call gravity, but we see that it's not really a force, merely a consequence of the curvature of spacetime.