Thanks fro asking the Apple Support Communities for help with adding music to your iMovie project. Please verify you are following the correct steps to complete this: iMovie for iOS (iPhone, iPod touch): Add audio
Also, verify you are using approved audio sources as shown here:
You can add background music, special effects, or your own recorded audio to iMovie.
Add background music stored on your device
You can add any of the following types of background music to a movie project:
Theme: Music that comes with each Apple-designed iMovie theme
iTunes: Songs from iTunes that have been synced to your device using iTunes on your computer
Imported: Songs that you created in GarageBand, Logic Pro X, or another app and imported into iMovie using iCloud Drive or iTunes on your computer. (To import background music from iCloud Drive, see “Add background music or other audio from iCloud Drive,” below.)
Note: Songs that appear dimmed or are marked Unavailable need to be downloaded to your device for use in iMovie. Use the Music app to download songs from iTunes in the Cloud, or use iTunes on your computer to sync songs from your iTunes library. If a song on your device still appears unavailable, it may be of a type that can’t be used in iMovie. For example, songs protected by digital rights management can’t be used in iMovie.
If you still have issues, please let us know what happens when you try the steps, and if you receive any alerts or error codes, please provide them to us. Thanks and have a wonderful day.