Replace -> Merge music

You should be able to do this with iTunes menu > Files > Library > Update iCloud Library if necessary. Mine does it automatically. Are you sure the songs are not already on your iPhone?

I see. You have two options.

1) What Apple would like you to do, Is to purchase iTunes Match. Then your personal music library (CDs) would be uploaded to iCloud and those songs would be available on your Phone like Apple Music is today. I use Match because the matched songs are played and downloaded, if you choose to make available offline, at 256k and some of my music is lower quality (old) so I get a better quality download. Caveat is that not all songs are matched so 10-20% will be your original recording quality. This percentage will be higher if you are into unique bands. Here is pretty good Article about iTunes Match from an independent perspective. Cost of Match is $25 a year.

2) Do it the old way. Turn off iCloud Match and sync your music the old way (pre iTunes 12.2). To turn off iCloud Match on iPhone Settings > iCloud uncheck Music. On Mac iTunes menu iTunes > Preferences > General uncheck iCloud Music Library. Then in iTunes Select Music with your iPhone connected by USB / Lightening cable and select the songs you want to have on your iPhone (Songs, playlists, albums) and sync. Then disconnect iPhone and reverse the steps above to turn iCloud Music back on.

I think this technique deletes downloaded iCloud Music so you have to do that over each time you add a CD. But some are okay with it since they no longer buy CDs and only have to upload the old CD collection once and plan to use Music or Apple Purchased Music for new music.