He was using some fancier and older form of English. I believe it is grammatically correct, we just don’t use those forms anymore. The first translation of the Gita is from 1785 and it is one of the most translated Asian texts. Famously, every translator places emphasis and projects their own personal worldview unto the text. Though Oppenheimer actually could read and had read the Bhagavad Gita in its original Sanskrit, so he was just giving it his own personal twist.

The original line comes from Chapter 11 Verse 32 of the Bhagavad Gita.

कालोऽस्मि लोकक्षयकृत्प्रवृद्धो

(kālo ’smi loka-kṣhaya-kṛit pravṛiddho)

The most literal translation would be: “I am mighty Time, the source of destruction of the worlds.” But काल can alternatively mean Death, and it looks like that’s the interpretation Oppenheimer chose. The verb here is a simple “am”, as in “I am Time/Death”. So the “am become” part is not due to any feature of Sanskrit itself.

But people usually take some liberty while translating poetry. Given the context (i.e. Krishna convincing Arjuna to fight, and showing him his true form), it makes sense to use “I have become” or even “I am become” (as explained in the other comments, it’s grammatically correct).