APA does not have official guidelines for citing a poem. It is possible, however, to gather some guidelines from the other materials in order to put together a poem citation. Generally, you will reference the source of the poem in the usual way - if you read the poem online, cite the website as the carrier, if you read it in a book then cite the book as the carrier, etc.
The year you quote should be the publication date of the source, not the date the poem was written, or first published. If the date of writing is significant, you could include it in your text.
From a single author collection of poetry
From an anthology of poetry using the "Chapter in an edited book" style
From the web
Citation in Text
You should refer to the name of the poem and the poet in the main body of your work, and include a citation to the anthology in which it appears.
Reference: Surname, Initial(s). ed(s). Year. Title. Edition (if not first edition). Place of publication: Publisher.
In the reference list/bibliography, refer only to the anthology in which the poem was published:
Reference: Poem Author’s Last name, First name. "Title of Poem.” Title of Collection, edited by Editor(s) First name, Last name, Edition, Publisher, Year of Publication. Page range.
Example: Jonson, Ben. "To the Memory of My Beloved, the Author Mr. William Shakespeare." The Norton Anthology of Poetry, edited by Alexander Allison et al., 3rd Edition, New York Norton, 1983. 239-40.
Note: In the full reference/Works Cited section, list the author's name as it appears in the work, i.e. last name and full first name or last name and initials.
There are two styles of MHRA referencing - footnotes and bibliography style and author-date style. Please check with your lecturer/tutor which one you must use.