This is a pretty un-GMAT-like question, and terrible for several reasons. Since "him" is doing the action, we need "he" and not "him." That's a totally fair test-able GMAT-rule. So normally our thinking on a GMAT question would go: (A) and (D) are out for Pronoun error.

BUT the word "but" is not always used as a conjunction. It can also be a preposition. And here's where we move outside of GMAT-land. When we use "but" to mean the same thing as "except" it's a preposition. And the object pronoun follows prepositions. So technically it's "him" here. Again, this is OUTSIDE the scope of the GMAT. That means it can only be either (A) or (D).

Since we don't say "Me was the thief," the correct answer is (A). So why do I REALLY not like this question? It looks like it's testing a GMAT rule (selecting subject/object pronouns), but instead it tests how a specific word can be multiple parts of speech. Not cool.

IMO C

IMO as Vivian said (the word "but" is not always used as a conjunction. It can also be a preposition)

here it acts as conjuction hence need not to be followed by objective pronoun "him" and "him" is the doer or subject of IC hence subjective form of "him" means "he" should be used and at last "I " acts as object of the IC so objective form of "I" means "me" is used at last

IMO C should be the ans