Yes. If you are an adult child, you may apply for and purchase a life insurance policy on your Father.
Adult children have an Insurable Interest on their parents. Insurable Interest is a requirement in anyone else you wish to insure for life insurance, other than yourself.
However, you may need your father's permission and signature on the application for life insurance, depending on the requirements of the insurance company.
Learn more about applying for life insurance on your Dad.