My son has a 5 yr old daughter. My son nor the mother were married. My son had a drug problem and is now off the drugs, but the mother still does drugs and leaves the child with anyone who will take her while she goes on her drug sprees or does the drugs in the home with the child present. We've contacted the dept of children and families in our town, and she's been drug tested many times, and has tested positive every time, but the dept still let the child stay in her custody. Is it possible for myself, being the grandparent to seek custody of this child or can my son. There are no custody papers but he pays child support weekly that was ordered through the court.

You can certainly try for guardianship of the child (I would go that route rather than custody). I would consult an attorney to help you