Magic armies examples in history?

There were numerous "divine visions" that the commanders relayed to their troops, as in Constantine did; one can call those beliefs in magical help, I guess.

The practice didn't quite end in medieval times. During WWI Russians used projectors to display an image of Virgin Mary on overhead clouds to convince the troops of divine support of their cause. From the viewpoint of an average semi-literate drafted soldier the appearance of Virgin Mary in the night skies would feel like magic. Couldn't quickly goodle a reference for that though.

It depends on your exact definition of magic. Magic in the broad sense was used a lot. Greek and Roman armies would never start a battle without a sacrifice. If the sacrifice was not accepted by the gods they would wait, then make another sacrifice etc. According to their accounts, magic was also used by barbarians. By Britons, for example. The use of magic by the ancient Jews is addressed in T. E. D.'s answer.

In the later, Christian times, they often used the sacred relics, icons, and other such things in the battles. Constantine won a crucial battle by a very simple tool: he just ordered his troops to pain crosses on their shields. To be sure he and most of his army were pagans, but the crosses helped nevertheless. He was so impressed by his own victory that later he converted to Christianity, or at least they say so. Same simple and effective tool was used by the (mostly pagan) Britons in the battle of Mount Badon where they routed Anglo-Saxons against enormous odds. I am not even mentioning the many victories of the later Christian armies achieved by similar means.

Similar magic methods are still widely used: https://www.youtube.com/watch?v=i1D09_l9j2w

https://www.youtube.com/watch?v=kmk-t-rzGRU

(Perhaps some people would say that Christian rites are different from magic, but on my opinion this is all the same). Probably many more battles in history where won with some sort of magic than without.

Here's an example of using science as magic. According to Herodotus, Thales of Miletus predicated a solar eclipse (some say lunar eclipse), possibly the one of May 28, 585 BC. This eclipse interrupted a battle between the Medes and the Lydians.

...just as the battle was growing warm, day was on a sudden changed into night. This event had been foretold by Thales, the Milesian, who forewarned the Ionians of it, fixing for it the very year in which it actually took place. The Medes and Lydians, when they observed the change, ceased fighting, and were alike anxious to have terms of peace agreed on.

I'm going to stretch "magic" and "army" a bit to gather in some of the more well documented modern examples.

In 1995, McArthur Wheeler walked into two Pittsburgh banks and robbed them in broad daylight, with no visible attempt at disguise. He was arrested later that night, less than an hour after videotapes of him taken from surveillance cameras were broadcast on the 11 o’clock news. When police later showed him the surveillance tapes, Mr. Wheeler stared in incredulity. “But I wore the juice” he mumbled. Apparently, Mr. Wheeler was under the impression that rubbing one’s face with lemon juice rendered it invisible to videotape cameras (Fuocco, 1996).

This is quoted in the paper "Unskilled and Unaware Of It" which we now know as the Dunning-Kruger Effect.

There are plenty of reports of police trying to use psychics to find lost children, often it turns out the psychic's role is overblown by the psychic themselves, or it's the actions of individual police officers not sanctioned by the department. This is an example of the latter where we have a report of Mexican police using voodoo to battle drug cartels.

More than 150 police officers have died throughout the area over the past few years.

As a result officers have attended the secret meetings that are said to draw on elements of Haitian Voodoo, Cuban Santeria and Mexican witchcraft.

“We know some agents use charms, saints and other methods for their protection," said Elias Alvarez, the Baja California federal Police Chief.

"They look for something to believe in."

This is a good illustration of the blurry line between religion and magic. I don't find this report much different than praying before a battle.

Here is an example of using magic to counter magic. During WWII Britain tried to turn people's belief in astrology into an asset by planting misleading (I suppose I should say "deliberately misleading") horoscopes in newspapers to counter those who predicted Nazi victory and Allied disaster.

[Louis de Wohl]'s task in the U.S. was to counter a convention of pro-German astrologers that had predicted Hitler would win the war. Billing himself as "The Modern Nostradamus," de Wohl proclaimed the stars showed the opposite — that Hitler would lose.

Source: Britain Used Astrologer In Fight Against Hitler

Lots. Probably the most well-known example is that the Jews used to take their God (inside the Arc of the Covenant) into battle with them. (Of course in their accounts, the magic often worked).

A much more modern version came out of the Ghost Dance of the late 19th Century. Through a combination of native and Mormon theological elements, a group of Lakota Warriors attempted to make themselves some bulletproof shirts. It didn't work out so hot for them. The incident is known today as the Wounded Knee Massacre.

Other similar attempts at being made bulletproof featured in the Boxer Rebellion, and of course the number of little superstitions and prayers employed by various people in all the wars of the 20th Century are too numerous to count. Hence the saying that "there are no atheists in foxholes."