Baha'is accept Abraham, Moses, Jesus and Muhammad as Manifestations of God and refer to the Bible and the Qur'an so yes I suppose we would be considered "Abrahamic".
"Among the great prophets was His Holiness Abraham who being an iconoclast and a herald of the oneness of God, was banished from His native land. He founded a family upon which the blessing of God descended; and it was owing to this religious basis and ordination that the Abrahamic house progressed and advanced. Through the divine benediction, noteworthy and luminous prophets issued from the lineage of His Holiness. There appeared Isaac, Ishmael, Jacob, Joseph, Moses, Aaron, David and Solomon. The Holy Land was conquered by the power of the Covenant of God with Abraham, and the glory of the Solomonic wisdom and sovereignty dawned. All this was due to the religion of God which this blessed lineage established and upheld. It is evident that throughout the history of Abraham and His posterity this was the source of their honor, advancement and civilization. Even today the descendants of His household and lineage are found throughout the world."
~ Abdu'l-Baha, Baha'i World Faith - p. 270