Actually, I just found the answer on the Warren website.
http://warren.ucsd.edu/residentlife/faq.php?faq_id=38
Q: How are single rooms assigned?
A: Single rooms are only available in our freshmen Residence Halls (Frankfurter, Harlan, and Stewart). After receiving your contract, Housing Administration will refer you to a website where you can enter your living preferences. Here you can indicate whether you would prefer to live in a single room. The computer system will randomly choose those students who will receive singles. Unfortunately, the demand for singles far exceeds the number of single rooms available so not all students who request a single room will be assigned to one. There are no singles available in the apartments (Black, Brennan, Douglas, and Goldberg).
Hopefully, it still holds true! haha