1.Apeaksoft Video Converter Ultimate https://www.apeaksoft.com/video-converter-ultimate/ is a professional tool to add music to iPhone videos. It contains many benefits than iTunes, such as:
Add background music to your videos with a few steps.
Process multiple videos at one time using the multi-thread.
Include extensive video editing tools, like crop, rotate, etc.
Protect and optimize video quality while adding music.
In a word, Video Converter Ultimate is the best way to add music to your iPhone videos without quality loss.
2.iMovie app is the video editor that developed by Apple for iPhone, iPad and MacOS. It is a free way to add music to a video, even the iMovie recorded video on iPhone. Moreover, it does not require a computer, although it cannot process large video files.
3.In addition to the iMovie app, there are several third-party apps designed for adding music on a video on iPhone. InShot, for example, is one of simple video editors for iOS that has the capacity to modify the background music of your videos.
You can learn more detailed steps by this article:https://www.apeaksoft.com/video-editing/add-music-to-a-video-iphone.html