It is highly unlikely that writing on the skin with ink would result in ink poisoning, according to Health Guidance. Most ballpoint pens do not contain toxic ink.
Health Guidance explains that older brands of ink pens and bottled ink often contains toxic ingredients, but it would take ingesting large amounts of this ink for serious ink poisoning to occur.
According to MedlinePlus, writing ink is made up of dyes, pigments, solvents and water. Symptoms of ink poisoning include eye irritation and staining of the skin and other mucous membranes. MedlinePlus also mentions that more than 1 ounce of writing ink needs to be consumed before a person requires medical treatment.