i know for sure that you can say:

Sacar una foto.

I'm not sure about desparar- but i would assume now from the 'shape' of the word. i'm pretty sure- not positive- that the root word of desparar has something to do with something leaving with great force (ex: a bullet).

The word is disparar, and the site dictionary does list one meaning as shooting a photograph. However, Kailey's suggestion is the one I've heard before. Might be regional'''?

RAE Dictionary does not list this meaning . . .

"Disparar" would be understood, if you can see the camera and you guess the intentions, but it is not a word we would use for pictures (in Spain, at least). You can say "disparar la cámara", and it is correct, but it sounds almost like "press the button to activate the (shutter) mechanism of the camera", and the same with the flash, but pictures don't have buttons.

My English-Spanish dictionary (Collins) does not translate "shoot (a picture)" as "disparar" neither.

In Colombia: sacar una foto
Also, in some areas close to the US: tomar una foto (probably because of the English influence of "take" a photo)