Not in any direct way. That is, it doesn’t provide an argument for the existence of God. But it does so indirectly, by providing an argument against the philosophy called materialism (or “physicalism”), which is the main intellectual opponent of belief in God in today’s world.
Materialism is an atheistic philosophy that says that all of reality is reducible to matter and its interactions. It has gained ground because many people think that it’s supported by science. They think that physics has shown the material world to be a closed system of cause and effect, sealed off from the influence of any non-physical realities — if any there be. Since our minds and thoughts obviously do affect the physical world, it would follow that they are themselves merely physical phenomena. No room for a spiritual soul or free will: for materialists we are just “machines made of meat.”
Quantum mechanics, however, throws a monkey wrench into this simple mechanical view of things. No less a figure than Eugene Wigner, a Nobel Prize winner in physics, claimed that materialism — at least with regard to the human mind — is not “logically consistent with present quantum mechanics.” And on the basis of quantum mechanics, Sir Rudolf Peierls, another great 20th-century physicist, said, “the premise that you can describe in terms of physics the whole function of a human being … including [his] knowledge, and [his] consciousness, is untenable. There is still something missing.”