Homecoming is coming up at my high school and my crush is a language fanatic, so it would be cool if I could have a poster asking "Will you be my homecoming date?" in Korean.
Is it a class, or a whole school homecoming?
동문회 = Homecoming for the whole school (literally 'same gate meeting')
동창회 = Homecoming for the class (literally 'same window meeting')
I'm not sure if saying 'will you be my date' literally would be natural. You could try saying 'shall we go together?' in a polite way:
동문회에 같이 가주시겠습니까?
which is something like 'will you do me the honor of accompanying me to the school homecoming'? (replace 동문회 with 동창회 if it's a class homecoming).