The 42-year-old, from Newport, was inspired to take up the sport by watching London 2012 and has already broken four world records and won team gold at the World Championships.
But this was his best performance yet as he showed solid form through the knockout rounds before beating David Dramoninsky of the Czech Republic in a closely-fought men's W1 individual final on Friday night - scoring a perfect 30 in the last set to win 141-139.
And Walker paid tribute to inspirational American archer Matt Stutzman, who uses his feet to fire arrows, for getting him hooked on the sport.
He said: "I feel on top of the world - this medal means everything and is the result of four years of hard work, and without the support of the National Lottery and its players none of this would be possible.
"During London 2012 I watched USA's Matt Stutzman and was so inspired by him I was desperate to give the sport a go and I've not looked back since."
Meanwhile, team-mate John Cavanagh lost in the first round while Jodie Grinham progressed to the quarter-finals of the women's event. Cavanagh said:
"It's disappointing but it was always going to be a difficult match. I started well and ended well but it just wasn't enough on the day.
"I've really enjoyed my time out in Rio and I'm looking forward to cheering on the rest of the ParalympicsGB team for the last couple of days."