You can! There are two options available to you. The first would be to choose your song via iTunes and play it through your phone while shooting your 360 video. There are two other ways you can dub music onto the 360 video file. The second option would be to shoot your video and then export it to iTunes or your computer, and choose a production software that allows you to layer music and video together. Production software programs include: iMovie, Final Cut, Premier Pro, etc.
After you have a completed, saved file, you can then upload it to Facebook or YouTube using the Chrome browser.