The shortlisting of her hit Anti-Hero makes Swift the first songwriter to score seven nominations in the category - overtaking Sir Paul McCartney and Lionel Richie, who have six each.
She is also nominated in the album and record of the year categories alongside Olivia Rodrigo, Miley Cyrus and SZA.
Lana Del Rey and Dua Lipa are among the other nominees for song of the year.
Billie Eilish, Jon Batiste and SZA have also been recognised in the category.
Swift's album of the year nod for Midnights is her sixth nomination in this category - and ties her with Barbra Streisand for the most nominations for a female artist.
If she wins, she will become the first artist to win album of the year four times.
More on the nominated artists:
It was harder for artists to make the Grammys shortlist this year due to new rules.
Organisers have cut the number of nominations available in each category from 10 to eight.
This year's Grammy Awards take place on 4 February in Los Angeles, with hosts yet to be announced.
British dance and electronic producer Fred Again is among the nominees for best new artist.
He is joined in the category by Gracie Abrams, Ice Spice, Jelly Roll, Coco Jones, Noah Kahan, Victoria Monet and War and Treaty.
US rapper and singer Jelly Roll might have been around since 2005 - but he scored a breakout single earlier this year with Need A Favor.
If the 38-year-old wins the award he will become the oldest person to be named best new artist - Sheryl Crow currently holds the record after picking it up aged 33.
Cyrus, Rodrigo, Swift, SZA, Batiste, Boygenius, Eilish and Monet are recognised on the record of the year shortlist.
Song of the year is different to record of the year - the former recognises songwriters and achievement in composition while the latter is concerned with the technical recording process - taking into account production, engineering and performance.
Many of the same artists are nominated for album of the year, with Swift, SZA, Rodrigo, Batiste, Boygenius and Cyrus all recognised alongside Janelle Monae and Lana Del Rey.
Nominations were announced on Friday, with singer-songwriter SZA leading the pack with nine in total.
She was recognised in the best progressive R&B album and best R&B performance categories.
SZA's collaboration with Phoebe Bridgers with Ghost in the Machine was nominated for best pop duo/group performance.
Bridgers' indie supergroup Boygenius was recognised in six categories too - including record of the year for Not Strong Enough and album of the year for The Record.
Boygenius, made up of Julien Baker, Lucy Dacus and Bridgers, first got together to debut a self-titled EP in 2018 and returned with new music earlier this year.
Monet has also had a strong showing - along with best new artist and record of the year for On My Mama she is also nominated for best R&B album for Jaguar II and best R&B performance for Hollywood.
Batiste was a surprise winner at last year's ceremony and features in the major categories once again, with his album World Music Radio and song Worship up for the top prizes.
Cyrus' nomination for Flowers in the song and record of the year categories and Endless Summer Vacation's album of the year nomination mark her first appearance in one of the major categories.
She previously had only received one nomination, for best pop album in 2015 for Bangerz.
Lana Del Rey has never won a Grammy before - but is recognised in five categories this year, including best alternative music album and best alternative music performance.
Rodrigo joins Eilish in achieving the feat of being nominated for best album, song and record for her first two studio albums.
The 20-year-old former Disney star's received chart success this year with song Vampire and album Guts.
Eilish has also featured heavily in this year's Grammy nominations - the song she made for the Barbie movie, What Was I Made For?, has made it onto the song and record of the year list.
The music from Barbie is well-represented across the nominations receiving 12 nods. Dua Lipa's Dance the Night, which is up for song of the year, features on the film's soundtrack.
Meanwhile Barbie World by Nicki Minaj and Ice Spice, and Ryan Gosling's I'm Just Ken, are up for best song written for visual media.
Country star Morgan Wallen only received one nod in the best country song category but didn't break through into any of the major ones.
His single Last Night topped the US charts for 16 weeks, with the track achieving the feat of the first country song by a male solo artist to reach number one in 42 years.
Wallen,who was criticisedover the use of a racial slur in 2022, also had chart success with his album One Thing At A Time earlier this year.
Doja Cat also didn't make it into any of the big categories - receiving nods for her song Attention in the best melodic rap performance and best rap song lists.
Paint the Town Red, which samples Dionne Warwick's Walk On By, was expected to make it onto the record of the year list but only managed the best pop performance category.
Earlier this year,BeyoncÃ© became the most decorated artistin Grammys history, winning four awards at the 65th ceremony - bringing her total haul to 32.
BBC Sounds: Annie Mac and Nick Grimshaw delve into the Grammy nominations onSidetracked.
Taylor Swift has broken a Grammys record with her latest nomination for song of the year.