Usually, this should be:
Instead, if you write:
Its meaning is considerably different, though it simply looks like the passive. It means both “My brother had my picture taken against my will and by force” and “My brother took the/a picture(s) I had (by force).” The reason is, I guess, that the core meaning of とる is to “take the control of something.”
However, there still remain unsolved problems. If とる means as the above one, it is almost the same as “take” in English, isn’t it? Moreover, is “I was taken a picture of by my brother” possible? If so, what is the difference from “I had a picture taken by my brother”?
I wonder if there is some similarity between “have something p.p.” and “もらう”.