Yes, the Milky Way galaxy, like many other galaxies, has a supermassive black hole at its center. This black hole is called Sagittarius A* (pronounced "Sagittarius A-star"). It is located in the constellation Sagittarius, hence the name.
Our solar system, including Earth, orbits around the center of the Milky Way galaxy, which is influenced by the gravitational pull of the combined mass of stars, gas, and dark matter within the galaxy. While the supermassive black hole at the center of the galaxy has a significant gravitational influence, it does not dictate the motion of individual stars or our solar system as a whole.
Instead, the gravitational forces from the collective mass of the galaxy, including the stars, gas, and dark matter, play a more substantial role in determining the orbits of stars and our solar system around the galactic center. The motion of stars in the galaxy is complex, and the overall dynamics are shaped by the distribution of mass throughout the galaxy.
So, while there is a supermassive black hole at the center of our galaxy, our orbit around the galactic center is influenced by the combined mass of the entire galaxy, not solely by the black hole itself.