The 1996 world champion, who is attending the World Series by Renault event because his son Josh is racing in the Formula Renault Eurocup this weekend, completed a handful of laps in the car.
It was the first time he had taken to the track in F1 machinery since he made his last start in the 1999 Japanese Grand Prix.
Hill told AUTOSPORT: "I spoke to Renault and said I'd be coming down because Josh was racing, and it kind of snowballed from there and I've ended up driving the Red Bull!
"You can't really say no to that, can you? So a big thanks to Renault and Red Bull."
Hill is the latest world champion to sample the RB6, after his former Williams team-mate Alain Prost demonstrated the car at the previous World Series by Renault round at Paul Ricard last month.
"I spoke to Alain after he drove it," Hill added. "Things have moved on a bit from when he stopped in '93, but these cars are quite similar to what I had in '99.
"Things like the hand clutch were already on the Jordan by then. The cars have changed subtly, but fundamentally they are the same.
"It's not a competition, there's no challenge, and I'm not being tested. It's purely for my own experience and it's fun."
The 52-year-old also paid tribute to Renault and Red Bull for staging so many demo runs though the season.
"It's great that they do this," he said. "They get a huge crown of people - a large proportion of which probably don't follow out sport that closely – and they are introduced to our sport.
"To have a Red Bull doing a few laps sells the whole sport to the fans. For them to see one car do a few laps... with an old fart in it… hopefully they will be inspired to follow the sport more widely."
- Red Bull