Merriam-Webster Online gathers several related senses of take:
11 b (1) : to obtain as the result of a special procedure : ascertain <take the temperature> <take a census> (2) : to get in or as if in writing <take notes> <take an inventory> (3) : to get by drawing or painting or by photography <take a snapshot> (4) : to get by transference from one surface to another <take a proof> <take fingerprints>
The common meaning here is to record something by procedure or writing instrument.
I hadn't previously seen the uses take a painting or take a drawing, so I consulted Google books and found that taking a drawing was common in the 1800s, during the rise of photography. This sense of take appears to have arisen in the late 1700s; note this example from The New-York Magazine or, Literary Repository (1792):
Mr. Peale, we hear, is engaged to take a painting of this extraordinary person, to preserve to future time the features and form of a person furnished with nerves and constitution to exist to so surprising an age, on that ocean of time which has long ago swallowed up so many millions of his contemporaries.
While making a drawing was always more common than taking one, I suspect that the latter usage took hold for photographs because the process of capturing (taking) a photograph is distinct from printing (making) it, and the taking happens when you open the shutter.