The quote is indeed from the Bhagavad Gita (“Song of the lord”). Some suggest it's a misquote, which would explain the peculiar grammar; but “am become” is not an error but a (poetic) archaism, as in “I am become a name, for always roaming with a hungry heart” (Tennyson, Ulysses). Which in turn might be a trace of French; “Je suis devenu la mort”.

Since Oppenheimer was proficient in sanskrit he read the original text, and the translation is his own; I haven't found any other translation with “am become”.
It certainly gives a certain something to the line, however, and it probably would have been less well known if it had been “I am death”.