The ringtone appears in When Sherlock calls the number on the pager found at the old lady's house, Moriarty doesn't answer with a voice. He answers with music. The specific track is "Stayin' Alive" by the Bee Gees .
[Link]
Listen to Jim Moriarty Ringtone (Official) by Sherlockholmesmoriarty in BBC❤❤❤ playlist online for free on SoundCloud. SoundCloud·Sherlockholmesmoriarty
Note: "Stayin' Alive" is a copyrighted song owned by the Bee Gees estates. While audio clips are widely shared online for personal use, be aware of copyright if you are using it for public content.