As Peter pointed out already, "wanna" should not be used when writing because it's ungrammatical. When we speak quickly, we tend to combine words together so that they sound like they're one word, but in writing, they still need to be separated into two. For instance: wanna, gonna (incorrect) = want to, going to (correct) kinda, sorta (incorrect) = kind of, sort of (correct) As for your question, the second one ("I want to take their picture") is correct. "Take them picture" doesn't make sense (unless you're using regional slang) because "them" is not a possessive word.

"wanna" is ungrammatical. It's the sort of slang used by teenagers in text messages.Never use it if you want to be taken seriously as a speaker of English and never use it any formal writing!

I wanna leap to the defense of "wanna" a bit, here. :) It's definitely very important to understand that the word is not, technically, correct. But you can certainly use it with intimates without hesitation. I'm CERTAIN that I've used it in emails and instant messages (via Skype for Business) to my direct manager and co-workers AFTER we'd established a mutual understanding and trust in one another's ability to use the language correctly. And that was when I was a professional writer. I think it depends what you're writing, and to whom. If in doubt, don't use it. Once that doubt goes away, go crazy! :)

Hi, you can say "I wanna take their picture" if you're using slang. :-)