I don't understand why it's "take a photo". Why take? Is there any rule for this?
It seems to be an extension of taking notes.
From "The Language of Photography" http://www.source.ie/issues/issues2140/issue22/is22artlanpho.html
To photograph exists alongside to take a photograph, to take a picture, and so on. This is an extension of a broad meaning of take 'to obtain or set down', as in taking notes or statements, 'to set down or get in writing'; more directly, it is an extension of a use recorded from the 17th century onwards in structures such as taking pictures, likenesses, or portraits 'to obtain or get a picture'. The specific photographic use seems to have driven out uses in relation to pictorial art - nowadays, we paint, draw, or produce portraits, and make or do drawings - so that taking a picture can only refer to photography.
In addition to the point made by Ronan, I think take belongs to the group of verbs that are semantically empty and are often christened delexical verbs. We often like to represent actions as nouns, often for maintaining an easy rhythm in speech.
So we 'take a walk', 'have/take a bath', 'have a read', 'have a look', 'take a dip', 'give a shove', 'give a laugh', 'make a promise' and so on.
In other words, don't think too much of the meaning of the verbs there!
Photography is about capturing the state of some photons within a moment (well, a very brief period of time). Once captured, the information about that state can be taken with you and reproduced anywhere. "Taking a photo" amounts to collecting information from the environment and carrying it away, i.e. literally the act of taking.
Peter provides some good examples of how "take" can be used in other scenarios where such reasoning doesn't make sense (I certainly don't carry a tub around with me whenever I "take a bath") but I think in this case, a literal meaning can and should be inferred.
I think my answer might be similar to Ronan's, but not enough to be a comment on that answer.
You can actually make photos as well, although to take a photo is more prevalent.
There are people on the Photography sub-site of StackExchange that determine their use based on what sort of action they are performing, noting subtle differences between to make and to take. See Does a photographer take pictures or make pictures?.
If we go back to painting we have words and expressions that offer the very same relationship between painter and subject. For example to 'capture a likeness'.
Then let's go back to earlier, to the word 'draw'. To draw means to pull. To draw a horse and cart. To take from one place to another. To withdraw money from one account to another.
This idea is the same in other languages. A portrait in Italian for example is 'ritratto', trarre (traere) means to pull/draw. The etymology of portrait would suggest it also means to take a likeness from where it is towards you now.
Interestingly how also photos were often initially viewed as 'stealing' part of you.
All in all, when we talk about reproducing what we see via pencil, paint or photo we are taking it from it is to where we are now.
There are only two verbs one can use in regards of using a camera to produce an image - 'take' and 'make'.
'Make' has am implied meaning of investing some effort - as in 'make dinner'. 'Take' feels more effortless.
Some years ago, photos were actually 'made' because it involved film processing, while now we just 'take' them.
A Chinese perspective:
In Chinese, one verb/noun can have totally different meanings. "take a photo" in Chinese is "拍照", "拍" means clap, "照" means "photo". In some province in China people say "捏一张" which also means "take a photo". "捏" means "pinch", "一张" means "one piece".
So, what I want to say is, sometimes an existing verb may be 'borrowed' to invent a new meaning. The existing meaning no longer suitable in new phrase.
Sometime the verb is not important, it just picked make a noun become a verb or action.