Mimers, often the birth time is not stated on the version of the birth certificate issued at the hospital; some states don't require a time of birth on official state copies of the birth certificate, but most do. One must contact the appropriate state agency and ask for a certified copy of the birth certificate, and specify that you want the one with the time of birth stated. Go to a website called
http://vitalchek.com, which lists contact agencies for every state in the US (and many other countries, as well).
If you were born in a locale which did not attach birth times to the certificate, contact the Medical Records department at the hospital where you were born and tell them that you want a copy of the facesheet of your infancy medical chart. There will be (probably on microfiche) a record of your mother's stay, which will specify the time of your birth somewhere within those pages, and a separate chart for you, as a new entity -- your birth time is considered the "time of admission," and so stated on the facesheet of that chart. Because of privacy rules regarding medical records, you will not be able to get a copy of your mother's record (only she can do that), but you will be able to otain your personal baby record.
It's best to get the birth time from a birth certificate or birth record, even though those are often off by several minutes; mothers are usually in no condition to remember to-the-minute birth times. Rectification is a very subjective process, and I personally do not trust it (though many others do).