No, a CD that carries the actual CD logo cannot have DRM. It is true that the music industry has often pushed 'enhanced' formats that look like CDs that do; SACD, for example.
Ownership is different to possession, and I want to actually own my music, not just possess the files.
There certainly are some services where you can legally download MP3 and FLAC files. Bandcamp, for example. If you download your music like that then, yes, you do own it.
But I'm not aware of anywhere you can get music from the major music labels nowadays (Amazon used to sell MP3s and so did Google Play Music, but neither does any more). If you do, I'd love to know.
On the other hand, you can still - although it's getting harder - buy CDs for major label artists and then you own the music (that copy of it).