No, there is no extra-biblical evidence of Abraham, nor is there really an expectation that there would be. There is a lot of other evidence, mostly in the forms of anachronisms, that indicate that Abraham was likely a composite account of a fictional progenitor that was compiled at a much later time. Perhaps the most glaring anachronism is the presence of the Philistines and their capital city Gerar, both of which are well out of place for that time period.

There is one piece of information that you might find relevant, although it's highly speculative. An Egyptian Stele from the 15th century BCE found in Beth Shean, near the Galilee, refers to a banu raham which means, children of Raham. Perhaps, there was an early tribe in the region named Raham, and it was later constructed that their progenitor was av raham the father of Raham. Source for this last point would be Liverani's Israel's History and the History of Israel.

For the first half you could look at really any history of Israel, Liverani would do, as would Finkelstein, Dever, Redford, etc. They all come to the conclusion that the patriarchs are ahistorical.