Repetition is usually used by poets to place emphasis on an idea. In this poem he would like you to think like he does about Annabel, to remember her as he does. It also creates a certain rhythm . Rhythm can contribute to the tone of the poem. This rhythm is very light and sweet like their love is.
I feel Poe used the repetition i Annabel Lee as a mental echo for himself and the reader. The poem recalls a childhood memory for him, as if beckoning him to his past. As he recalls her, his language simplifies to that of a child or a more simple time, bringing in fantasy icons which would be familiar to a child from fairy tales or stories/fables. The repetition also represents a continued strong tie between Poe and Annabel Lee.
I agree with Daisy from Memphis! I think we can go further and argue that Poe almost certainly uses repetition as a literary device in "Annabel Lee" in order to conjure the feeling of being haunted and to convey the sense of being obsessively in love.