Addiction touches every family. One person's addiction severely impacted the lives of 2 people I love dearly.  Even though the choice to abuse drugs/alcohol is the responsibility of the person, once it it's satanic grip, it becomes more like possession.  Thus, I implored St. Michael for intercession, with great success.
I'm not familiar with a specific traditional prayer related to drug addiction.  Others here much smarter than me may have that information, but I did look up traditional non controversial patron saints associated with addiction:
St. John of God
St. Martin of Tours
St. Matthias the Apostle
St. Monica
St. Urban of Langres

Combined with St. Michael, that's a mighty force.
Your charity to pray on behalf of your loved one is a beautiful act of mercy.

The rosary is always good advice.