I am 16 and sexually active. Do I need a pap smear to get a prescription for birth control?

No. Pap smears are indicated 3 years after beginning sexual activity or at age 21 (whichever comes first). You do not need one for a physician to prescribe birth control, nor do you need parental consent. However, it is recommended that you are honest with your parents about your sexual activity. Be sure to always use condoms. Birth control pills do not prevent sexually transmitted infections.
No. You should be able to get contraception without a pap smear. Current recommendations for pap smear screening is to begin at the age of 21.