What if my child’s father is a registered sex offender, can I terminate his rights?

DCF will be involved. Whether they remove this child depends heavily on why you lost other children and your current circumstances. Have you addressed and remedied the issues causing the termination of your parental rights? Removing the child from your custody at birth by court (shelter) order does not terminate your rights. But DCF may go that direction. Your actions influence decisions by DCF, and judges. If you are not stable, drug free and having prenatal health care, then you have some work to do. Be proactive, get some advice. Find a lawyer now who practices dependency law in your area and review your case.