It's good of you to be looking after your father. And it's a near certainty that you can purchase life insurance on him.
What you're describing is a concept called "insurable interest." In other words, does a child have an insurable interest in the life of their parent?
Life insurance is regulated at the state level and states may differ on what they consider an insurable interest. Understandably, regulation arose to protect people from financial speculation on their lives through insurance.
But generally speaking, a child does have an insurable interest in the life of their parent. And this would be especially so for the purpose you described...making sure that your dad is cared for at his death.
Presumably, you'd own the policy with your father as the insured. Depending on the type of policy, he will have to answer various questions and may need to undergo some medical requirements.
Hope that helps. All the best.