Laurence Olivier in the title role of his film of Hamlet in 1948.

He was also nominated for Henry V (1946), Richard III (1956) and Othello (1965). Other Shakespearean nominees include Norma Shearer (Juliet), Basil Rathbone (Tybalt), Jean Simmons (Ophelia), Marlon Brando (Marc Antony), Maggie Smith (Desdemona), Joyce Redman (Emilia), Frank Finlay (Iago), Kenneth Branagh (Henry V) and Denzel Washington (Macbeth).

Other Oscar-winning performances that included large sections of Shakespeare are Ronald Colman in A Double Life and Gwynneth Paltrow in Shakespeare in Love, which featured the actors performing scenes from Othello and Romeo & Juliet, respectively.

The role of Bernardo in West Side Story won an Oscar for George Chakiras and is loosely based on Tybalt in Romeo & Juliet. Too loosely to correctly answer this question, but you are permitted a pang of smug righteous indignation if you feel slighted by its omission. Rita Moreno (1961) and Ariana DeBose's (2021) Oscar-winning performances of Anita doesn't really have a corresponding role in Shakespeare's play, so you're on your own if you thought that should be the answer.