This page contains all the information you need on how to have a romance with James Vega.
James is an option available to only Female Shepard. Once you’ve returned to the Normandy after the mission, Priority: Mars, speak with James on the lowest floor. During the conversation say “I’m looking now”, “I sure can…”, and “Lola? I like that”. Keep speaking to him regularly after missions and agreeing with his opinions, then invite him up to the Cabin to chat privately.
Here you’ll want to say the following, “I thought about it”, “You still did the right thing”, and “Hell, yeah”. Continue the game some more and once you’ve completed the mission, Priority: Citadel, speak with James at the Docks: Holding Area and choose the following choices, “Welcome to the program”, “Don’t let yourself down”.