The aquila was a Roman standard bearing an eagle and somethimes the letters SPQR. As well as having a military function, the aquila was a totem and as usch had a religious function. The aquila was kept in a shrine called the aedes along with the imago, which was a three dimesional metal portrait of the emperor. The letters SPQR, meaning the senate and people of Rome, identified the eagle with Rome itself.
While the imago, being a physical representation of the emperor, was directly associated with the imperial cult which held that he was divine or semi-divine, the eagle itself was a symbol of the fighting spirit of the legion or of the might of Rome. Soldiers of the Roman Empire swore an oath to the emperor, so the religious aspect of the oath was another link between the empire and the eagleas a totem.
Augustus Caesar (born Gaius Octavius), was the first Roman Emperor, and the imperial cult began in 14CE when, after his death, the Senate declared him to be a god. Prior to his death Augustus held the title of Pontifex Maximus, or chief priest. While the rejection of the imagio by the Jewish population as an object of idolatory was documented by Josephus (The Wars of the Jews, book 2, chapter 9), a similar identification of the aquila depends on an examination of the nature of idolatory according to Judaism.
In Exodus chapter 20 there are described two qualities of an idol. Firstly, that it is an image of something from the air, sea or earth, and secondly that obesience or service is paid to it. As well as physical idols made of wood or metal, Ezekiel chapter 14 describes idols of the heart. In the Hebrew idiom the heart is the seat of the mind, so an idol of the heart is a mental construct, for example the belief that an ordinary man is a divine being.
The question of whether or not the emperors of the imperial cult were divine in terms of Hebrew thought is easily answered in the negative, both from the reaction of the Jews to the imagines (as documented by Josephus) and from the tribute passage of the gospels, in which a clear distinction is made between Caesar and deity. It follows that obesience or service to the emperor was idolatory if he was considered to a deity, which in general was the case. Therefore in the context of the imperial cult, the Roman eagle was a symbol of idolatory, although it wasn't itself an idol unless obsesience or service was paid to it.
The book of Jasher describes how Abram gained favour by rejecting his father's idols. This story is particularly relevant becuase it recounts how the tradition of idolatory was established by Nimrod, who was king at the time of the iconstruction of the tower of Babel. The Hebrew word for Babel is the same as for Babylon, and Rome is called Babylon in the Bible.