The Sun does indeed have an orbit within our galaxy, but within our solar system, it can be considered as sitting relatively stationary at the center. Let me explain further:
The Sun is the central star of our solar system, and it exerts a powerful gravitational force that keeps all the planets, moons, asteroids, and other objects in orbit around it. From the perspective of the solar system, it appears as if the Sun is stationary, and all the other objects are moving around it.
However, on a larger scale, our entire solar system, including the Sun, is in motion within the Milky Way galaxy. The Sun, along with all the other stars in the galaxy, orbits around the galactic center. It takes approximately 225-250 million years for the Sun to complete one orbit around the center of the Milky Way.
So, while the Sun is fixed at the center of our solar system, it is not completely motionless. It is constantly in motion as it orbits around the galactic center together with all the other stars in our galaxy.