Yes, Jupiter's massive size and gravitational pull do have an effect on the surrounding spacetime. According to Einstein's theory of general relativity, massive objects like Jupiter can warp the fabric of spacetime around them. This warping of spacetime is what we perceive as gravity.
Jupiter's gravity is so strong that it can significantly bend the trajectory of nearby objects, including light. This effect is known as gravitational lensing. It occurs when the path of light is curved as it passes through the gravitational field of a massive object. Gravitational lensing has been observed and studied by astronomers as a means to study distant galaxies and other celestial objects.
However, it's important to note that the warping of spacetime by Jupiter is a relatively small-scale effect compared to extremely massive objects like black holes. Jupiter's gravitational field is significant within its immediate vicinity, affecting its moons and nearby space probes, but its influence diminishes with distance.