Identify the poetic device used in the following line from John Keats' "On First Looking into Chapman's Homer."Is "That deep-brow'd Homer" an example of personification or an allusion?
That line is most definitely an allusion and not personifcation.
Personification is when you are talking about an inanimate object and you give it human characteristics. For example, you could say that the line about the planet "swimming" is personification because planets don't swim.
But the line you mention is allusion. It is referring to someone (in this case, the poet Homer) that everyone who reads the poem is likely to have heard of. Homer was a very famous Greek poet and, in the time that Keats was writing, any educated person would have known who he was.
In addition to the allusion to Homer, the description of Homer is metaphoric, as well. "The deep-brow'd Homer" refers to Homer's brillancy as Keats is highly impressed with both his intellectual capacity and his purity. [We use the word deep to mean the same as in "deep thought," and "deep thinker."] In a previous line, Homer's association with Apollo, also glorifies him.
Keats's "On First Looking into Chapman's Homer" is a precisely written sonnet in which each word has been selected to be in perfect poetic diction.