No, getting a Pap smear will not affect your period. Two tools are used to take a Pap sample, one called a spatula, the other a cytobrush. This second tool looks like a mascara brush and is used to scrape cells from your cervix. Sometimes mild bleeding or spotting can occur with this scraping, but this is not your period. Having your period can interfere with the Pap sample, so assure you are not menstruating the day of your appointment. Easier said than done, I know. Too often seems that our period will show up just when the appointment we have been waiting for does!
As far as I know, a Pap smear doesn’t affect your uterus enough to alter your period. If you do notice anything different after your exam (other than a bit of spotting or bleeding, which isn’t uncommon), be sure and tell your healthcare professional. Also, be sure to check out Michelle’s answer, as I’m sure she has more definitive information.
I’ve had quite a few Pap smears, all at different points in my cycle. Though, I prefer to plan ahead and schedule my appointments after my period is done. I’m honestly not sure how or even if it might affect your period. You should see what our Health Expert, Michelle, has to say about this.