The song, named Won't Forget, entered the UK iTunes Top 20 within 48 hours of release.
The single is fronted by former Britain's Got Talent winner Jai McDowall, with backing music by four Glasgow policemen.
Jai, from Ayrshire, said: "It's my first top 20 hit. My mum texted me and said that I was in the top 20 and I've been checking it all day."
Police constables Paul Keenan, Jamie Easton, Craig Brooks and Stephen Marlin, wrote the song and it was produced by students at the SAE music school in Kinning Park.