In order to buy life insurance on someone's life you need an insurable interest in that person.
Insurable Interest basically means you stand to lose financially if the person were to die, or you rely on the person for some means of financial support.
There does exist insurable interest between a father and son, spouses, siblings, parents and children, business partners, etc.
That means you can buy life insurance for your father naming him as the insured person on the life insurance.
You would be responsible for paying the premiums and you would want to name yourself as the beneficiary to receive the death benefit upon the death of your father.
However, in order to buy the life insurance you will need your father's permission, signature on the application, and he may need to answer some health questions or even submit to a physical exam - which is paid for by the life insurance company.
In addition, there are some life insurance companies that allow you to apply online and purchase life insurance direct, without any health exam required. Here's how you may buy life insurance with no exam for your father.