If she is really into songs, yes, sharing a romantic song with her as a way to begin the conversation may work.
Just make sure that it isn’t a song that indirectly references your relationship with her.
Sending her a song like this would only remind her about why she is upset with you and you could end up making her angry again.
Choose a song that has nothing to do with the current situation that you are in with her.
This should help to create a new space in her mind that isn’t consumed with her disapproval of how you have behaved in the past.