Yes, an unmarried woman can adopt a child in India. The Applicants must be between the ages of 25-55; financially capable; physically, mentally and emotionally stable and without any life-threatening conditions.
Under Hindu adoption and maintenance act, an unmarried women can adopt a child if she is adult and is of sound mind. If the woman wants to adopt a male child , there should be age difference of 21 years.
In Muslim, Christian and Parsi personal laws adoption is not permitted. So in their case Guardianship and wards act is applicable.