In general I think this could be a good idea.
There are a couple ways to do this.
You could co-own this with your parents and have all of you on the mortgage and on the deed.
Basically, you would be using your credit to get the loan as a co-signer.
You would have to draw up a contract determining how to share gained equity over time.
You could split the proceeds of the eventual sale of the home. You need to figure out how to use the tax deductins, etc.
Co-signing is a way to actually help your parents get a house rather then renting.
But there are may complications and there could be issues down the road.
The other way, as you said, would to be buy the home in your name and rent it to them.
If you feel they will make the payments then you would be OK. They've been making their payments already anyway.
You would have to set up the loan as an investment property which is a more difficult loan to get.
But if you can it could work out well for you.
It doesn't do much for them equity wise but it would be an upgrade from where they were living and they would be working with you if they wanted to do any updates on the house.
In time, you can build some equity and payment history on the investment property.
With that, you will be able to buy your own home when you are ready. You can have mortgages on two houses if you show that you can pay for them both.
Then you would have two sources of equity building.
At some point, your parents would move out or move on and you could sell it for a profit.
Right now, someone owns the place where your parents are living and they are building equity on that property.
Maybe you could be the one building that equity instead.