Yup I started when I was 12! I would suggest getting training at the Red Cross before starting the job though, it makes you look like you know what you're doing (cause you do) and sometimes people pay more!
I was allowed to start at 12. Check your state and city laws on the subject. You can even google "how old to babysit in ____state or city____: and look on the list for a 'gov' site! It will be most accurate.