Can you download ringtones directly to iphone 4 without a computer or jailbreak?

I want to download a new ringtone on my iphone 4. I don't own a computer or have access to one. Is there a way I can get ringtones for free and not have to sync on a computer? I know it is possible on a droid phone, what about iphone?

Yes. Plenty of options out there in Appstore that you can download to phone itself.
See this example
Best luck.
https://itunes.apple.com/...08399?mt=8