Yes, yes they were.

The Polycarp of Martyrdom, usually dated to the mid-to-late 2nd century, refers to this in the case of other martyrs, and holds it out as a threat to Polycarp. (source in translation)

The third century text, the Passion of Perpetua and Felicty features the death of martyrs sentences to the beasts in Carthage (source in translation)

I was just looking over the wikipedia page on Damnatio Ad Bestias, it is troublingly vague and hand-waving in its references to things like "widespread view", "specialists".

It's worth pointing out that Damnatio ad Bestias was a typical punishment for criminals, which is the category Christians fell into when prosecuted, there was nothing special about ad bestias for them.

Fine, in light of the discussion, I offer a revised answer with discussion of the primary texts, explanation and critique of Moss, and an indication of where to follow up the current state of play in Late Antique research into Martyrdom accounts.

Were Christians put to death by beasts (Damnatio ad bestias) before the Edict of Milan?

Firstly, we have no real historical case to make in this answer as to whether ‘fighting the beasts’ was a punishment in the circus. This is well established. The only question is whether this penalty was applied to Christians. What sort of evidences can we supply?

First we should understand the context in which Christians were tried in the Roman Empire. The literary exchange between Pliny the Younger and the Emperor Trajan in Pliny, Letters 10.96-97 is one of the earliest mentions of Christians. Pliny was governor in Bityhnia 111-113 AD and discusses with Trajan what to do about Christians. It appears from these two letters (one from Pliny, the other a reply from Trajan) that the confession of being a Christian is itself enough to be condemned for.

In the 2nd century we begin to get Christian literature in the categories of Passiones (i.e. accounts of suffering/martyrdom) and Acta (purported records of the trial and testimony of Christians before the courts. For believers, such documents served to provide rhetorical examples of Christian idealism, insofar as martyrdom came to be seen as an act of loyalty to Christ that united the martyr with Christ in his suffering.

The Martyrdom of Polycarp is one such early text; it presents as a letter from the church of Smyrna to the one in Philomelion, giving an account of Polycarp’s death. The author’s particular desire is to show how this martyrdom is ‘according to the pattern of the Gospel’, and there are many points at which the narrative construction mirrors or echoes Christ’s death. Condemnation to beasts in mentioned at several points. In chapter 4, Quintus who is a counter-example, looses his nerve when he faces the beasts. In chapter 11, the pro-consul who is attempting to persuade Polycarp to recant, threatens punishment by beasts, which Polycarp does not fear. Chapter 12 mentions that he cannot be condemned to the beasts, since the games were closed. This is noteworthy, because the Games were not put on in order to kill Christians, rather when there were Games and Christians in prison to be killed, they could be executed in this fashion.

The Passion of Perpetua and Felicity is another early text, typically dated to early 3rd century. It appears to be composed by 4 authors: (1) a final redactor (very possibly Tertullian), (2) a first person account by Perpetua, (3) another vision account by Saturus, (4) an eye-witness account of the martyrdoms. Much of the text is taken up by accounts of particular visions relating to the martyrs, which the overall author has a particular interest in recording for posterity. In the prefatory material the collector mentions the purpose of such texts: to be a public remembrance of what they did as well as an encouragement for the faith to other believers. The final portions of the text recount the martyrs facing several beasts, including a leopard, bear, boar, and cow. The details of the Games accord with what is generally known about damnatio ad bestias, and despite the rhetorical construction there is no particular reason to doubt that such punishments were used for Christians.

An undisputed text on martyrdom is written by Tertullian, likely datable to 197AD. Tertullian’s rhetoric is aimed at strengthening Christians at the beginning of a persecution to face the threats and remain loyal for the goal of martyrdom. He refers to beasts several times as among the punishments that they may face, and should not fear. Beasts appear alongside the sword, fire, and tortures as forms of punishment.

Not all martyrdoms were by the beasts, of course. Polycarp’s account has him die eventually by a blade, having attempted to burn him alive. In the Acts of martyrdom of Justin and his companions, they are summarily beheaded. The text of the Letter to the churches of Vienna and Lyons (ca. 178AD) records that some were indeed to face beasts in the amphitheatre, including Maturus, Sanctus, Blandina, and Attalus. This was in combination with other punishments. Also in this letter a distinction is made, those among the confessors with Roman citizenship were to be beheaded (a more typical punishment for a citizen), those without citizen rights would face the beasts.

The most critical work on Christian martyrdom in recent years is the 2013 book, “The Myth of Persecution” by Candida Moss. Among her arguments are that since all accounts are written later and by Christians, it is impossible to lend them any credence. This is a difficult argument to counter, but likewise a difficult position to swallow. The reality of rhetorical purpose, deliberate literary devices, etc., does not necessarily detract from historical fidelity. It is one thing to recognise that a text has been shaped for a rhetorical purpose, it is another to say that rhetorical purpose renders a text into nothing more than a ‘pious fiction’. Likewise Moss includes a number of strict conditions to make something ‘qualify’ as martyrdom: it must be solely for the fact of being a Christian, and persecution can only be understood as specific targeting of Christians. The fact that Decius, for instance, passed legislation requiring acts of worship that Christians wouldn’t follow, disqualifies the events under Decius from the title ‘persecution’. This, likewise, is perhaps playing with definitions. By Moss’s definitions there was only ‘real’ persecution under Diocletian, and only very few ‘true’ martyrs: those who were free from suicidal tendencies, militant understandings, and any form of self-interest. The general critique of Moss’s work includes the refrain that even though we may assess these primary texts critically, the mere fact of emendations or literary flourishes does not invalidate historical value. If it did, we wouldn’t do any historical work with Christian texts at all.

What Moss’s work fails to do is argue that Christian martyrdom ‘never happened at all’. And if it happened, it is well within the scope of historical probability that it included death by the beasts. Indeed, it would be historically improbable that such a form of punishment was excluded from convicted Christians.

What sort of other evidence might we want? The great difficulty is that of surviving documentation. While Romans certainly were great record keepers, no one particularly made an effort to transcribe through the centuries court documentation. Apart from the exceptional remains in Egypt, a great deal of everyday documents have not survived. Scribes and later monks were primarily interested in copying and preserving religious, philosophical, and occasionally literary texts. It is no particular surprise to find a dearth of specifically Roman legal material dealing with martyrdoms. Among what we do have from Egypt are accounts that depict various legal dealings of Christians with authorities, which tend on the whole to ratify the realism of Christians having property seized and being unable to effectively participate in the legal system during some periods of persecution, due to requirements to sacrifice.

Perhaps ironically, the best introduction to contemporary studies in martyrdom is by Moss herself, her article ‘Current trends in the study of early Christian martyrdom’ from Bulletin for the Study of Religion, 2012. It is along the lines of a summary of the ‘state of play’ in martyrdom research, and reveals that the question of whether martyrdom occurred is not a current point of controversy.