Can A Not Confident Person Become A Teacher?

Confidence comes from experience and how well you know the subject you are talking about. I have the same fear as you about talking in public. I teach pain management in a hospital to all staff. I feel nervous all the time when I start talking in front of a new group, but it goes away after a few minutes. The reason it goes away is because I know my subject and I am comfortable teaching it. Once I did a grand rounds in front of 110 doctors and nurses. I thought I was going to have a heart attack. But, after a few moments I relaxed and really did a good job. I got a standing ovation when I finished. That helped my confidence alot, But I still get nervous  when I start talking in front a a new group. That's ok, because I know in a few moments, it will go away.

Asilverman is absolutely right, but I'd like to add that If you truly have a passion to teach, it probably won't take long to get over your lack of confidence.  It will also be gratifying to know that you're imparting your knowledge to others.  It might help too, if you took a public speaking class.  I believe that many people, myself included, get nervous about speaking in public.  I'm sure you'll do just fine, and you'll have a long, happy career, doing what you want to do.  Best of luck.  

Well you could do the teacher training - that might help you to feel more confident. If by the end of qualifying and training to teach you still feel you can't do it, then why not become a tutor instead, and teach one-to-one.

Yes actually they can. Anyone can become a teacher. But, let me say this, soon people that are not confident start a job not confident, but as you get comfortable with it then you will be more confident.