His previous worst round was an 81 in the 2002 Open at Muirfield, a round completed in a storm that made scoring difficult.
Woods, who carded a two-over-par 73 in his opening round, missed much of last season, including the Ryder Cup, after having back surgery in March 2014.
"We all have days like this," he said. "Unfortunately mine was in a public forum and a public setting, but we all have days like this and we take the good with the bad."
Laird, 32, who shot a second straight 66 in wet and windy conditions, said: "It was a very Scottish day today with the misty drizzle. The big thing was I drove well."
American Daniel Berger is two shots behind Laird on eight under, while another tour rookie, Justin Thomas, is third on seven under.
Phil Mickelson, a three-time winner in Phoenix, missed the cut after carding a second-round five-over 76.