Annett underwent surgery for a fractured and dislocated sternum last week and is expected to be out six to eight weeks.
Sorenson will drive the No. 43 Richard Petty Motorsports car beginning this week at Las Vegas.
"It's an unfortunate situation for the team and Michael," Sorenson said in a team release. "I have been to the hospital to see him, and he will be fine, but it's going to take some time to heal. As a friend for a long time, my initial reaction was concern. I'm glad that he's recovering now.''
Annett was involved in an 11-car accident on lap 116. He was taken to Halifax Health in Daytona Beach and kept overnight for evaluation. Aric Almirola replaced him last week at Phoenix.
"I talked to him about it, and he really wants to see me do well,'' Sorenson said. "This is a big deal for me, and I am going to make the most of it."