How do i cite an encyclical as a source?
I cannot offer any specific advice on citations, however I am going to give you a few links to consider. You may also check out the writing center to see if they might be able to help you specifically. Of course, any information you receive, you should always run by your professor to make sure it's in agreement with what they are seeking. I hope this helps.
This page, from the University of Portland, is actually a document they put together on how to cite Catholic documents.
This page from University of San Diego has some great examples toward the bottom of the page. You can search for encyclical once you are on the page to take you right to that area: