I purchased song on ITunes and clicked the download button already but the song didn't show in . . . so I can't choose that song to set up for ringtone.
When you purchased song on ITunes check your Music Library -> Recently added.
If you can't find it, try to redownload, see -> Redownload music -> Redownload music - Apple Support
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To make and/or use a song as a ringtone, you must first make that song suitable for a ringtone.
See the following Apple articles:
Create and manage ringtones -> Create and manage ringtones - Apple Community
Create a ringtone of your Logic Pro or GarageBand for Mac song
Create a ringtone of your Logic Pro or GarageBand for Mac song – Apple Support (UK)
Create Ringtones in Garageband -> Create Ringtones in Garageband - Apple Community