The 11-year-old's recording of If Every Day Was Christmas received its first radio play on Wednesday before being made available online.
Profits from the song's sales will go to Global's Make Some Noise charity, which supports disadvantaged young people in the UK.
Beckham is being managed by Scooter Braun - who also signed Justin Bieber.
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Bieber was 13 years old when he released his first single One Time in 2009.
Earlier this week, the young Beckham launched his own Instagram account, where he has been posting images to promote the single.
He also used the page to upload videos of himself singing. In one clip, he is seen performing a cover of Hopeful by Twista featuring Faith Evans.
Beckham Jr also uploaded a cover of When I'm Gone - originally recorded in 1931 by the Carter Family but made famous more recently by Anna Kendrick, who performed it in the film Pitch Perfect.
Speaking to Capital presenter Dave Berry about his debut single, the 11-year-old said it combined "two of my favourite things - singing and Christmas".
His father David, who was in the room when he was being interviewed, said he was "really proud" of his son for venturing into music, adding: "He's having fun, he's enjoying it."
But the move was criticised by Good Morning Britain host Piers Morgan, who said: "Why don't you go to school, mate, because you're not famous, your parents are famous... stop putting these kids into the public domain while simultaneously saying privacy."
Scooter Braun hit back on Twitter, saying of Cruz: "He is an 11-year-old who wanted to make a song to help other kids. Once again Piers shows why he is a jackass and why his [US] show was cancelled.
"Some people in this world make a living out of finding the worst in every situation. It means they have a career... not class. Just a career."
Last week, Beckham's older brother Brooklyn announced he is to release his own photography book.
Cruz Beckham, the son of David and Victoria Beckham, has released his debut single.