Can stopping birth control make your period irregular?

Yes, it's normal for your menstrual cycle to be irregular once you come off hormonal Birth Control.

While on hormonal birth control your menstrual cycles are suppressed in order to stop ovulation occurring, once you come off hormonal birth control it takes time for your body to start ovulating on a regular basis again. It's a little like going through puberty all over again, or if you had irregular cycles prior to going on hormonal birth control because the issue wasn't treated it may return once you stop using the birth control. Your cycle may continue to be irregular for up to a year.