Roberts was born in The Bronx, New York City of Irish and Jewish descent, Her father sold ink pens.At age 15, she abandoned her studies to get married and lived for a while hitch-hiking across the United States until her mother-in-law annulled the unionTanya lived with her mother in Toronto for several years where she started formulating a photo portfolio and laying plans for a career She moved to New York City and became a highly sought after fashion and cover model.
After meeting psychology student Barry Roberts while waiting in line for a movie, she soon married again, having proposed to him in a subway station. While Barry started a career as a screenwriter, Tanya began to study at the Actors Studio with Lee Strasberg and Uta Hagen.
Roberts began as a model in television advertisements for Ultra Brite, Clairol and Cool Ray sunglasses. She played serious roles in the Off Broadway productions Picnic and Antigone. In between TV ads and theater gigs, she supported herself as an Arthur Murray dance instructor. Her film debut was the 1975 thriller Forced Entry. This was followed in 1976 by the comedy The Yum-Yum Girls.
In 1977, as her husband was securing his own screenwriting career, the couple moved to Hollywood. The following year, Roberts participated in the drama Fingers. A role in the 1979 cult-movie Tourist Trap followed. Also in 1979, she appeared in the films Racket and California Dreaming.
Roberts also featured in several television pilots that were never picked up: Pleasure Cove, the 1978 comedy Zuma Beach and Waikiki (1980).
In 1980, Roberts was chosen among 2,000 candidates to replace Shelley Hack in the television series Charlie's Angels for what would be the last season of the series. In the show, Roberts interpreted her character Julie Rogers as a streetwise fighter who used her fists more than her gun. She was featured on the cover of People magazine and offered more ambitious projects. In 1982, she played Kiri in The Beastmaster. She appeared in a nude pictorial in Playboy to help promote the movie, appearing on that issue's cover (October 1982).
In 1983, Roberts filmed the Italian-made and little-known adventure Paladini-storia d'armi e d'amori ("Paladins—the story of love and arms"), also known as Hearts and Armour, based on the medieval novel Orlando Furioso. It also starred Ronn Moss of The Bold and the Beautiful.
She played the role of Velda, a buxom secretary to private detective Mike Hammer in the television movie Murder Me, Murder You, the first of two pilots that spawned the syndicated television series Mickey Spillane's Mike Hammer. Roberts declined to continue the role in the Mike Hammer series so she could film her next project, Sheena: Queen of the Jungle. The 1984 film was based on a character adapted from a Will Eisner's comic book. Dressed in scantily clad costumes, Sheena also introduced a new blonde hairstyle that Roberts would keep for the rest of her career. The movie became a box office disaster and was mauled by critics. Her subsequent appearance as Bond girl Stacey Sutton in A View to a Kill (1985) provided many scenes with Roger Moore as an articulate and educated geologist.
After a brief break, Roberts career took a downturn. Her films included Body Slam (1987), an action movie set in the professional wrestling world. Roberts closed out the decade with Purgatory, a movie about a woman wrongly imprisoned in Africa.
In 1991 she starred in the soft porn thriller Inner Sanctum alongside Margaux Hemingway. In 1992, she played Kay Egan in Sins of Desire.
Roberts also appeared on the cable TV series Hot Line (1994) and the video game The Pandora Directive (1996).
In 1998, she became familiar to younger audiences when she took on the role of Midge Pinciotti on the television sitcom That '70s Show. In an interview on E! True Hollywood Story discussing That '70s Show, Roberts said she left the series in 2001 because her husband had become terminally ill.
In 2008, Roberts wrote the foreword to the book, The Q Guide to Charlie's Angels by Mike Pingel.