No, the Sun does not orbit the Earth. In our solar system, the Sun is at the center, and the planets, including Earth, orbit around it. The motion of the Earth and other planets around the Sun is due to the gravitational force exerted by the Sun.
However, it's worth noting that the Sun and other celestial bodies do experience slight gravitational interactions with each other. These interactions can cause a small wobble or oscillation in the Sun's motion, but this wobble is primarily influenced by the gravitational pull of other massive objects in the solar system, such as the gas giants Jupiter and Saturn. These interactions can be measured and have been observed, contributing to our understanding of the dynamics of the solar system.
But in terms of the Sun's overall motion, it remains at the center of the solar system and provides the gravitational force that keeps the Earth and other planets in orbit around it.