Yes, one App to get free ringtones on the iPhone is Ringtones for iPhone & Ringtone Maker by byss mobile.
Lifewire shares these 10 Great Free iPhone Ringtones Apps you can look up on iTunes:
1. Create Ringtones
2. Ringtones 500000+
3. Ringtone Converter
4. Ringtone Designer
5. Ringtone DJ
6. Ringtone Maker
7. Ringtone Maker Free
8. Ringtones Free
9. Ringtones for iPhone
10. Zed.ge Ringtones
Check out these Top 10 Awesome Ringtones Ever compiled by KeepVid Pro.