In 2023, Dickinson stated that she had a 20-year on-and-off affair with Frank Sinatra, and that he was the love of her life and "one of the most charismatic men that ever was" . Dickinson had a relationship with musician Billy Vera in the 1980s and appeared in the music video for his single "I Can Take Care of Myself".

Dickinson, the second of four daughters, was born Angeline Brown in Kulm, North Dakota, the daughter of Frederica and Leo H. Brown. Her family is of German descent and she was raised Roman Catholic.

She has appeared in over 50 major movies and television productions, but is most known for her roles in "Police Woman" and "Dressed to Kill." Among her many accolades, Angie has a star on Hollywood's Walk of Fame and her work in "Police Woman" earned her a Golden Globe for Best Actress in a Dramatic Series.

She came in second at a local preliminary for the Miss America contest, and that got the attention of a casting agent, who landed her a spot as one of six long-stemmed showgirls on The Jimmy Durante Show. That's where she met Frank Sinatra, who was a guest star on the television show.