According to the Quran, Abraham was given a scripture just like Moses.
This is certainly ˹mentioned˺ in the earlier Scriptures— the Scriptures of Abraham and Moses. [Quran 87/18-19]
The scripture of Moses, I believe is the Torah. However, what could be the scripture of Abraham? Was Abraham given a scripture according to the Jewish tradition? If so, do we still have access to it?
Abraham was not given any scripture. According to our tradition, he did write books, so maybe that is what it's referring to. To quote Maimonides:
And, on this path the world continued its course of circuity until the birth of the firmest pillar of the world, Abraham our father. As soon as this giant was weaned he commenced to busy his mind, in his infancy he commenced to think by day and by night, and would encounter this enigma: How is it possible that this planet should continuously be in motion and have no leader—and who, indeed, causes it to revolve, it being impossible that it should revolve itself? Moreover, he neither had a teacher nor one to impart aught to him, for he was sunk in Ur of the Chaldeans among the foolish worshipers of stars, and his father, and his mother, like all the people, worshiped stars, and he, although following them in their worship, busies his heart and reflects until he attains the path of truth, and, by his correct thinking, he understood when he finally saw the line of righteousness. He knew that there is One God; He leads the planet; He created everything; and in all that is there is no god save He. He knew that the whole world was in error, and that the thing which caused them to err was, that their worshiping the stars and the images brought about the loss of the truth from their consciousness. And, when Abraham was forty years old he recognized his Creator. After he came to this comprehension and knowledge he started to confute the sons of Ur of the Chaldeans, and to organize disputations with them, cautioning them, saying: "This is not the true path that you are following", and he destroyed the images, and commenced preaching to the people warning them that it is not right to worship any save the God of the universe, and unto Him alone it is right to bow down, to offer sacrifices, and compound offerings, so that the creatures of the future shall recognize Him. Moreover, it is right to destroy and break in pieces all of the images, so that the whole population of the future be not led to an error like unto these who imagine that there is no God save these images. When he had them subdued by his well supported contentions, the king tried to put him to death, but he was saved by a miracle, and went hence to Haran. There he stood up anew and called out in a great voice to the whole world, to let them know that there is One God for the whole universe, and unto Him it is proper to render service. And thus he went onward with his proclamations from city to city, and from government to government, until he attained the land of Canaan amidst his outcry, even as it is said: "And called there on the name of the Lord, the Everlasting God" (Gen. 21.33). When the people who congregated about him asked him concerning his preachments, he replied by imparting knowledge to each and every one according to his mentality, to the end that he was able to turn him to the path of truth, until there congregated about him thousands, even tens of thousands, and they became the people of Abraham's household, in whose heart he implanted this great cause, concerning which he compiled books, and which he imparted to his son Isaac.
As far as I know none of those books are extant.
It could be that the book of Genesis would be referred to as the Book of Abraham. We find that this book is referred to as a book separate from the rest of the Torah according to Rashi in two places:
וַיִּקַּח֙ סֵ֣פֶר הַבְּרִ֔ית וַיִּקְרָ֖א בְּאָזְנֵ֣י הָעָ֑ם וַיֹּ֣אמְר֔וּ כֹּ֛ל אֲשֶׁר־דִּבֶּ֥ר יְהוָ֖ה נַעֲשֶׂ֥ה וְנִשְׁמָֽע׃
Then he took the record of the covenant and read it aloud to the people. And they said, “All that the LORD has spoken we will faithfully do!”
ספר הברית. מִבְּרֵאשִׁית וְעַד מַתַּן תּוֹרָה וּמִצְווֹת שֶׁנִּצְטַוּוּ בְמָרָה:
וַיֹּ֕אמֶר לְלַמֵּ֥ד בְּנֵֽי־יְהוּדָ֖ה קָ֑שֶׁת הִנֵּ֥ה כְתוּבָ֖ה עַל־סֵ֥פֶר הַיָּשָֽׁר׃
He ordered the Judites to be taught [The Song of the] Bow. It is recorded in the Book of Jashar.
הנה כתובה על ספר הישר. הלא היא כתובה על ספר בראשית שהיא ספר ישרים אברהם יצחק ויעקב.
