No. Edgar Allan Poe's poem "Annabel Lee" is full of figurative language, but it has no similes.
Similes are figurative comparisons using the word "like" or "as." If Poe had written, for example, that "The moon beams like a memory," or "Her eyes are as bright as stars," then those expressions would be called similes because they would compare one thing to another thing using "like" or "as." But again, Poe didn't write those examples in the poem; there are no similes in "Annabel Lee."
Consider how a simile is just one type of comparison. Interestingly, the poem contains plenty of other figurative comparisons. For example, in the second stanza, the speaker claims that he and Annabel "loved with a love that was more than love." Saying that their love was somehow more than love is a comparison: a way of saying that one thing is more or less intense than another thing. But it's not a simile, which always expresses instead how one thing is equally intense as another thing.
Aside from comparisons like those, "Annabel Lee" also boasts plenty of imagery and hyperbole. It's a highly figurative, richly dramatic poem; it just happens to lack similes!