* Missing article: You need the definite article "the" before "man" to make the sentence grammatically correct.
* Word order: The sentence structure is a bit awkward. It would be more natural to put the relative clause ("who I took a picture of") before the noun it modifies.
Here's how to correct the sentence:
This is the man who I took a picture of.
You could also rephrase the sentence:
This is the man I took a picture of.