Since you are speaking about a poem it would be the narrator if the poem has one in it.
If you are speaking about the poet you would say the writer.
You also have those who recite poetry that is written by others. When "so and so" recited the poem "so" written by Frost, they brought to life...
He's the author of "Monster Slayer". I have read some on line reviews about his books and I keep coming up with a so so writer.
What is your opinion on the Author?