The 18-year-old had his first tattoo etched on to his forearm by his father's friend, Mark Mahoney, at the Shamrock Social Club in Los Angeles.
It is similar to one former footballer David has on his left arm.
Brooklyn shared a series of black-and-white images of the process on Instagram.
"Honoured to have my first tattoo done by dads friend Mark Mahoney," he told his 9.6 million followers on the social networking site.
He continued: "Thank you so much Mark x just like dads."
David is thought to have accompanied his eldest son to the tattoo studio, where he has had work done himself.
The star is a fan of tattoos and has around 40 designs inked on his body.