Video shows Norman leaping over a bull inside a bullring during the event.
Afterward, Norman posted videos on his Instagram stories, saying a number of times that the experience was "crazy."
"I had to face the bull straight on," he said. "It was fun. It was worth it. It was really worth it."
Norman also tweeted a photo from the bullring.
In 2016, Norman, then with the Carolina Panthers, told WCCB in Charlotte, North Carolina, that running with the bulls was on his list of possible offseason activities.
Five people have been gored during this year's bull runs, which began Sunday. The nine-day San Fermin fiesta attracts partygoers and bull aficionados from around the world.