Both sentences are correct (with the addition of "a," as below), but
they mean different things.
"Can you take a photo OF us?" means that you are asking the person to
take a photo which will show you. You will appear in the picture.
"Can you take a photo FOR us?" means that you are asking the person to
take a photo that you would otherwise have taken yourself. In other words,
this person will be holding your camera and taking a picture of someone
or something, not necessarily you.
"For somebody" often indicates a service performed for a person. For
example:
I'm sorry you're sick today. Can I get something for you at the
market?
Sam can't drive for several weeks because he broke his leg, so his
wife is driving for him.
Can you deliver this package for me? Thanks a lot.
Julie