Elizabeth Taylor has signed a contract to do a book. It won't be a kiss-and-tell autobiography, and it won't be a diet or exercise manual. The superstar has signed with G.P. Putnam's Sons and Berkley Press for an undisclosed sum for her personal view of women's attitudes toward weight gain and loss and the ways in which they affect a woman's image and self esteem. This could be a new trend: self-analysis of the stars. A hardback edition is expected out next year.

Taylor was quoted by her publishers as saying "It has been many years since I wrote a book and I'm thrilled and excited about this new endeaver. I wrote my first book when I was 12 years old, entitled 'Nibbles and Me.' " It was published in 1946. Her second book, "Elizabeth Taylor, An Informal Memoir," was published in 1964. By contract, Taylor will travel and appear on the various television talk shows to promote the book. Think of the fun she'll have discussing diets with Joan Rivers on the "Tonight" show. No writer has been named yet to work with Taylor on the project. It's a safe bet it won't be Taylor's unofficial biographer Kitty Kelley. Amy Carter's Apartheid Protest

Amy Carter, the 18-year-old daughter of former president Jimmy Carter, sat in Providence, R.I., District Court yesterday among accused prostitutes, thieves and shoplifters before pleading innocent to charges that were later dropped for participating in an antiapartheid sit-in at the IBM Corp. The Brown University freshman and 13 others were arrested Wednesday while demonstrating in IBM's Provincetown office, protesting what they said was IBM's nearly $100 million investment in South Africa and company support of South Africa's policy of racial separation.

Charges against the 14 students were dropped yesterday at the request of IBM "for business reasons." A spokesman for IBM said the corporation is opposed to South Africa's policy of racial separation and is working to change the apartheid system. Leaving the hearing with fists held high, the students marched hand-in-hand through downtown streets singing "We Shall Overcome." Amy, who has been a member of the Rhode Island Free South Africa Coalition since entering Brown, said, "If my father hadn't been Jimmy Carter, I still would have done this today." She was arrested here last April at a demonstration at the South African Embassy. A spokesman for the Carters said her parents would not be commenting on this incident. Good Hands at the White House

It might easily be said yesterday that the president met with two men who have good hands. President Reagan had meetings with two different artists, Marvelous Marvin Hagler, world middleweight champion, and the great pianist Vladimir Horowitz. They were not at the same meeting. Hagler met with the president to be congratulated for his 12th successful defense of his title March 10.

Horowitz was there as the first major American performer to perform in the Soviet Union as part of the new cultural exchange agreement the president signed at the Geneva Summit. The 81-year-old Horowitz, who will leave next month on the trip, will perform in Leningrad and Moscow. It will mark the first time he has been in the Soviet Union since he left there 60 years ago. End Notes

If you watch the hot television series "Miami Vice" you might in some future episode catch a glimpse of Washingtonians Florenz and Nan Ourisman. Ourisman, a former vice president and owner of Ourisman Chevrolet, has a home in Palm Beach, Fla. It was at a Planned Parenthood fund-raising auction there that he bid $2,700 for the opportunity play a walk-on part. They haven't filmed their spot yet. The show called them once when they were unable to make the shooting . . .

Viking Press agreed to an out-of-court settlement to satisfy a suit brought by the widow of a man who claimed Pulitzer Prize-winning author William Kennedy had libeled her and her husband. Marie Maguire of Albany claimed an anecdote in Kennedy's "O Albany!" libeled her and her husband John Maguire, who died in January. A passage recounts a story that John Maguire supposedly told about receiving money to vote a certain way in an election. Maguire's lawyer said the story was untrue. Kennedy said the incident was "unnecessary." He said a phone call from Maguire would have been enough to eliminate the story. Kennedy and Maguire were Albany Times Union reporters in the 1950s . . .