How to get music from a CD to an iPhone

I have an iPhone SE with Apple Music and a Windows PC (Windows 11) with iTunes. When I purchase music from the iTunes store, it automatically goes to my iPhone. But when I import music into iTunes from a CD, it doesn't. When I connect my iPhone to my PC with a USB cable, my iPhone appears in iTunes, but when I try to drag the music over to it, or copy and paste the music, nothing happens. I can't figure out how to get music from a CD onto my iPhone. Does it require some sort of special USB cable? Would very much appreciate any help. Thanks.