Step 2. Tap the three-dot menu icon to the right of the song title, then tap "Add to My Music".
Step 3. Go to the alarm clock app, set a new alarm, then tap the "Sound" button in the settings". Find the song that you've previously selected in the Apple Music app by navigating through the "Artists" or "Genres" sections.
Note that if you'll opt for this method, the song will be streamed from Apple Music. As such, you may want to make sure you're on your Wi-Fi connection before turning in for the night. Otherwise, your iPhone/iPad will stream the song through your data connection, which may hurt your quota or incur additional charges.