Lady A and Zac Brown Band are next with six nominations apiece, while Swift and Eric Church took five nods each for the third annual fan-voted awards.
Bryan, Swift, Lady A, Zac Brown Band, and Jason Aldean are up for the night's top honor, artist of the year. Bryan also has nominations in the male artist, album, single, and video of the year categories.
Dierks Bentley's "Home," Church's "Chief," Lady A's "Own the Night," and Blake Shelton's "Red River Blue" join Bryan's "tailgates & tanlines" on the album of the year list. Hit song "I Don't Want This Night To End" nabbed Bryan single and video of the year nominations.
Miranda Lambert's popular trio Pistol Annies is nominated in the new artist category with Lauren Alaina, Hunter Hayes, Jana Kramer, and Kip Moore.
The ACAs air Dec. 10 on Fox. Voting is open on the show's Web site.
Elvis Costello, B.B. King, and Ray Davies are among the nominees for the 2013 Songwriters Hall of Fame.
They're joined by a slew of top acts, including Jimmy Buffett, Vince Gill, and Rod Temperton, who wrote Michael Jackson's "Thriller," "Rock With You," and "Off the Wall."
Songwriters Hall provided a list of nominees in advance of the official announcement, set for Tuesday. The gala is June 13 in New York.
Also nominated are Fleetwood Mac's Stevie Nicks, Lindsey Buckingham, and Christine McVie, former Eurythmics bandmates Annie Lennox and Dave Stewart, Jeff Lynne, Steve Winwood, Aerosmith's Steven Tyler and Joe Perry, Bobby Womack, and Foreigner's Lou Gramm and Mick Jones.
Voting ends Dec. 17.
Led Zeppelin will not be reuniting anytime soon.
That message came through loud and clear Tuesday. Just the mention of the topic set off lead singer Robert Plant at a news conference for the band's upcoming concert film, Celebration Day.
At the film's premiere later in the evening, guitarist Jimmy Page set the record straight, sort of, about a potential reunion.
"I think it's disappointing for people when the answer is no," Page said. But he later added: "That's what it is now."