English lit journals publishing graduate-level works
Theoretically, your status as student, senior lecturer or professor should not matter in terms of publish in a journal. If your idea is original and your research is relevant and situated in the current debates of the scientific community, then try to publish your texts. Talk to your professors or supervisors about it and tell them about your plan. Maybe, they have suggestions and can give you feedback on the text that you have in mind for submission.  Nevertheless, keep in mind, that your term paper or master thesis is not a journal article. I guess, you have to do a lot to rewriting and re-structuring your text that it will eventually become a published article. Moreover, publishing a text takes a lot of time (from submitting to the final version to get an onlinefirst publication, it can take 1-2 years). I don't know in which year of your master program you are, but eventually, the publication might happen after you are already accepted as a PhD candidate ;) 

There are probably student-run journals who especially address young scholars to submit their papers. For this, just google... 
 Literally, I just searched for it and found 2 websites which might be relevant for you: https://complit.fas.harvard.edu/journalsconferences-graduate-students and http://www.highpoint.edu/urcw/student-journal-publishing-opportunities-politics-international-affairs-law-2/