Depending on your personality, you could make any major "outgoing". However, to more specifically answer your question, I would personally recommend Public Relations. Public speaking most definitely relies on individuals who are not afraid to get in front of small-large groups of people to discuss topics.
According to study.com, "Public relations majors can find employment in a number of settings, including professional services companies, nonprofit organizations, government agencies and educational institutions. A bachelor's degree in public relations can lead to a variety of job opportunities, including public relations specialist, media planner, media relations specialist, strategic planner, social media manager, marketing assistant, marketing coordinator, marketing communications specialist, account executive and copywriter."
The Public Relations major is usually either combined with Marketing and/or Advertising majors as well. I have personally found that having studied Public Relations, it opened the doors to opportunities of speaking to and building numerous relationships with people throughout my career. If you are a truly outgoing and extroverted individual, I think that Public Relations is definitely an avenue that would interest you.
Good luck in your future endeavors!