This page contains all the information you need on how to have a romance with James Vega.
Securing the romance
Once you’ve completed the necessary steps to continuing the romance with James which can be found here, How To Start James Romance. Invite James to your Apartment at the Citadel via the Terminal and say “Maybe I’m interested in you” during the conversation.
During the party, speak with James as soon as you find him and say “Support Hook Up” and then regularly speak with him as the party continues. Finally, you’ll wake up next to James at the end of the party and your romance will finish.