Daniel Day-Lewis is nominated for the Best Actor award for his performance in the film's title role as the US president who led his country through the civil war and ended slavery.
The film picked up 10 nominations in total, with nine each for Les Miserables and Life Of Pi.
Bardem's performance as Bond villain Raoul Silva in Skyfall has been recognised with a nomination for Supporting Actor along with Day-Lewis' Lincoln co-star Tommy Lee Jones, Alan Arkin, Christoph Waltz and Philip Seymour Hoffman.
His Bond co-star, Dame Judi Dench, is nominated for Best Supporting Actress for her role as spy master M in the same film, which has eight nominations.
She faces competition from Anne Hathaway who is nominated for her role in the big screen version of Les Miserables.
Also nominated are Amy Adams for The Master, Helen Hunt for The Sessions and another of Lincoln's stars - Sally Field who plays the president's wife.
Dame Helen Mirren is nominated in the Best Actress category for her role in Hitchcock - playing the wife of the filmmaker.
She is joined on the shortlist by Amour star Emmanuelle Riva, Jennifer Lawrence who is recognised for Silver Linings Playbook, Rust and Bone's Marion Cotillard and Jessica Chastain for Zero Dark Thirty.
Quentin Tarantino is nominated for Best Director and Original Screenplay for his western Django Unchained.
The award for best film sees Lincoln and Les Miserables up against Affleck's Argo, Life Of Pi and Zero Dark Thirty - the story of the manhunt for Osama bin Laden.
Les Miserables is also in with a chance to win Outstanding British Film along with Anna Karenina, The Best Exotic Marigold Hotel, Seven Psychopaths and the latest Bond.
Skyfall is nominated for Outstanding British Film and Original Music and also picks up nods for Cinematography, Editing, Production Design and Sound.
TV star Dexter Fletcher is nominated for an Outstanding Debut award - with his co-writer Danny King - for their work on Wild Bill.