Identifying music that you downloaded to your phone using Google Music can be difficult, because the tracks are saved in an obscure menu under a coded filename. The directory is /storage/sdcard0/Android/data/com.google.android.music/files/music. The only way to figure out which one of those coded files is your ringtone is to play each one (or try to deduce it from the download date).
I suggest going to Google Music on your desktop, finding your ringtone, and downloading it there. The mp3 that downloads to your computer will have the actual filename, and you can then transfer it to your phone via USB cable, wirelessly, or using Google Drive. Move it to the Ringtones folder as described above.