Since your question is not limited only to arguments of Shankara, I am going to explain an argument in this answer. But I am not sure whether this has been used by anyone or not to argue against the anatman view.
Buddhist view accepts existence of Karma and rebirth. And it is a simple principle of the system of Karma that the doer of the action and the experiencer of the results, both are the same person. And when a person dies, he takes birth again to experience the results of his unexpereinced actions. Now the question is, what is common between the deceased person and the reborn one that you say this new born one is the reincarnation of the deceased one?
Certainly, the body is not common, nor also the mind. If the mind were common, then the new born one would have the exact same tendencies and memories. So when the body and mind are not common, then certainly there must be something else common between the two that their reincarnation is accepted. And Hinduism says, it is the atman that is common in both the bodies. But as per Buddhism there is this missing gap.
So if we accept anatman view then the question of identity would arise. Buddhists just say the new body is an effect of actions done by the past body. But effect being something different than the cause, there identity should not be accepted. But nevertheless they do so. For example, His Holiness Dalai Lama is believed to reincarnate once He leaves His old body. Hence, after the death of His Holiness, they start the search for His Holiness's reincarnation.
I don't know any textual reference but I believe Buddha just didn't acknowledge the existence of Atman. He didn't completely deny it's existence. The existence of an eternal self can cause attachment in people's mind. And because attachment of any form leads to suffering, Buddha didn't acknowledge its existence. Because the concept of whole of Buddhism is to reduce suffering. During His time in Hinduism yajna, animal sacrifices, etc. were high in practice for the purpose of acquiring a good position for the atman in the afterlife . It is probably because of that He preached an anatman view.