Is there a way that I can become and get paid to care for ill step father who lives in my home?

He can certainly pay you to take care of him. If he cannot afford that and is on Medicaid then they may approve him for home care & if it’s a self directed program he can choose you as the caregiver and you will be paid. It’s minimum wage in most states with no benefits and would likely be no more than 20-40 hours a week. If your state of Arizona uses carrying agencies to prove home care for Medicaid recipients then you could try to get a job at one and ask them to assign you to your step dad.

I believe that different states have different rules, so you would need to check out what applies where you live. Is your stepfather able to make a formal caregiver's contract with you? - that should make everything easier, to begin with.

I am talking about what happens if your stepfather pays you, by the way. State/social security benefits for family members looking after relatives tend to be pretty hard to come by.