Scott was born in Wise, Virginia, the son of Helena Agnes (née Slemp; 1904–1935) and F. Scott (1896–1948). He was the only son and younger of their two children. His mother died just before his eighth birthday, and he was raised by his father, an executive at the Buick Motor Company. Scott's great-uncle was Republican U.S. Representative C. Bascom Slemp of Virginia.

As a young man, Scott's original ambition was to be a writer like his favorite author, F. Scott Fitzgerald, and while in high school, he wrote many short stories, none of which were ever published. As an adult, he tried on many occasions to write a novel, but was never able to complete one to his satisfaction. When asked by an interviewer in later life which contemporary novelists he admired, he replied, "I stopped reading novels when I stopped trying to write them."

Scott joined the US Marines, serving from 1945 until 1949, and was assigned to the prestigious 8th and I Barracks in Washington, D.C. In that capacity, he served as a guard at Arlington National Cemetery and taught English literature and radio speaking/writing at the Marine Corps Institute. He later said that his duties at Arlington led to his drinking.

After his military service, Scott enrolled in the University of Missouri, where he majored in journalism and then became interested in drama; he left college after a year to pursue acting. In voice, appearance, and personality, many say he resembled the Minnesota politician and baseball magnate Bob Short.[citation needed]

Scott first rose to prominence for his work with Joseph Papp's New York Shakespeare Festival. In 1958, he won an Obie Award for his performances in Children of Darkness (in which he made the first of many appearances opposite his future wife, actress Colleen Dewhurst), for As You Like It, and for playing Richard III of England to particular acclaim in Shakespeare's Richard III (a performance one critic said was the "angriest" Richard III of all time). He was on Broadway the following year, winning critical acclaim for his portrayal of the prosecutor in The Andersonville Trial by Saul Levitt. This was based on the military trial of the commandant of the infamous Civil War prison camp in Andersonville, Georgia. His performance earned him a mention in Time magazine as a rising young actor of great intensity.[citation needed] In 1970 Scott directed a highly acclaimed television version of this same play. It starred William Shatner, Richard Basehart, and Jack Cassidy, who was nominated for an Emmy Award for his performance as the defense lawyer in this production.

Scott continued to appear in and sometimes direct Broadway productions throughout the 1960s. The most commercially successful show he worked on was Neil Simon's Plaza Suite (1968), composed of three separate one-act plays all utilizing the same set, which ran for 1097 performances. Scott played a different lead role in each act.

Scott appeared in many television series too, including the 1962 role of Arthur Lilly in the episode "The Brazen Bell" in the NBC western series The Virginian, in which he recites Oscar Wilde's poem "The Ballad Of Reading Gaol". That same year, he appeared as Anton Novak in the episode entitled "I Don't Belong in a White-Painted House" on NBC's medical drama about psychiatry, The Eleventh Hour, starring Wendell Corey and Jack Ging.

In 1963, Scott was top billed in the critically acclaimed[citation needed] CBS hour-long drama series East Side, West Side; he and co-star Cicely Tyson played urban social workers. The show lasted only one season. In 1966, Scott appeared as Jud Barker in the NBC western The Road West, starring Barry Sullivan, Kathryn Hays, Andrew Prine, and Glenn Corbett.

Scott won wide public recognition in the film Anatomy of a Murder, in which he played a wily prosecutor opposite James Stewart as the defense attorney. Scott was nominated for an Academy Award for Best Supporting Actor.

Scott's most famous early role was in Dr. Strangelove, or How I Learned to Stop Worrying and Love the Bomb, where he played the part of General "Buck" Turgidson. It is revealed on the DVD documentary that after having shot many takes of any given scene, Stanley Kubrick would frequently ask Scott to redo it in an "over the top" fashion. Kubrick would then proceed to use this version in the final cut, which Scott supposedly resented. However, Kubrick did earn Scott's respect on this film, since by that time Scott was an accomplished chess player.[citation needed] The cast and crew noted that they would often play chess between takes, and Kubrick was the only person who could routinely beat him.[citation needed]