Yes, the gas giants in our solar system, such as Jupiter and Saturn, do have an effect on the fabric of spacetime. According to Einstein's theory of general relativity, mass and energy curve spacetime, causing objects to follow curved paths in the presence of gravitational fields. This curvature is responsible for the phenomenon we perceive as gravity.
Gas giants like Jupiter and Saturn have large masses, which means they have significant gravitational fields. These massive bodies cause a distortion in the spacetime around them. As a result, objects, including light, passing near these gas giants will experience gravitational effects, including the bending of their trajectories.
The bending of light around massive objects, known as gravitational lensing, is a well-known effect predicted by general relativity. It has been observed and confirmed through various astronomical observations. In the case of gas giants, their gravitational fields can cause the light from distant stars to bend as it passes near them.
It's important to note that the bending of spacetime around gas giants is relatively small compared to the curvature caused by extremely massive objects like black holes. Nevertheless, gas giants still have a measurable effect on the fabric of spacetime in their vicinity.