应该是：
May I have a photo(picture) taken with you?
因为你要和别人合影,肯定不是自己拿着相机在拍.
have sth done 表示”请（让）某人做某事学长，我用的自己的相机。就是今天在广场上遇见一个超帅的外国帅哥，想 上去合张影，不知道怎么表达~~，求学长指教。。谢谢就说：
May I have a photo(picture) taken with you?
Would you mind having a photo taken with me?
Would you be so kind as to have a picture taken with me?
Would you be kind enough to have a picture taken with me?