It is believed that there is a black hole at the centre of the Milky Way galaxy. And the sun revolves around the centre of the milky way. So does it mean our sun is revolving around the centre of the galaxy due to this black hole?
The Sun orbits in the entire Galactic gravitational potential, which is very approximately similar to that provided by considering that all the mass interior to its Galactic orbit (about 100 billion solar masses) were concentrated at the Galactic centre.
The black hole at the centre has a mass of 4 million Suns, so contributes less than 0.01% of the mass required to keep the Sun in its present Galactic orbit of about 200 million years. Or to put it another way, if the Sun just orbited the black hole with a period of 200 million years, we would need to be about 800 light years from the Galactic centre, rather than the 30,000 light years we presently are.
Yes, of course. In the same way as the answer to If the Moon revolves around Earth, does it mean it revolves around you? is Yes!
This does not mean, though, that you determine or even significantly affect the orbit of the Moon, and so it is with the supermassive black hole (SMBH) at the center of the Milky Way and the orbit of the Sun, as Rob explains (but fails to answer your question ;-).
The gravitational tug of the Milky Way at the Sun is the sum of the tugs of all its components, not just the SMBH. This is dominated by the vast number of stars (and dark matter), which together weight much more than the SMBH.