Work on your image. As you are starting out in the acting world, it is unlikely you have an image consultant at your disposal. Ask female friends what they think of your style. How would they would describe you? Are you the good-looking geek? The rugged sports jock? Romantic actors tend to be type cast. Work out which stereotype you most resemble and work towards achieving this image fully.
Take acting classes. Think about taking drama at college or, if you are already working, take active classes in the evening. Ask tutors what type of romantic roles they think you are suitable for. Listen to their advice and act on it...literally.
Research romantic actors such as Brad Pitt, George Clooney and Johnny Depp. Find out how they got their first breaks. Try and learn from their life stories. Network with people involved in producing romantic comedies.
Go to auditions. You are never going to become a romantic actor if nobody knows who you are. Audition for any parts going. Don't be too selective. Hearththrobs start out in the most unlikely of places. Matt Le Blanc was in a Heinz Ketchup ad, for example. It is more important that you get on screen if you want to become a romantic actor, than to wait for a plum role to come along.