Elizabeth Taylor, who has had almost as many fiance's as fabulous jewels, has a new one of each:

* The fiance' is Dennis Stein, a public relations consultant with MacAndrews & Forbes, a Technicolor subsidiary, who lives in New York and works on both coasts. Both he and Taylor are 52. Stein told WABC-TV in New York that "Elizabeth has a magic wand of happiness that she has struck me with."

* The jewel is a blue sapphire, about 20 carats, surrounded by diamonds, and rumored to have been purchased from Harry Winston Inc., which has supplied most of her legendary gems. Ronald Winston, now head of the company, said he was not free to comment.

The ring is somewhat larger than the 16 1/2-carat sapphire surrounded by diamonds that her former fiance', Victor Gonzalez Luna, gave her in August 1983. In 1979 she sold a 60.42-carat diamond, one of the many remarkable diamonds given her by former-former husband Richard Burton. Her most recent husband, Sen. John Warner (R-Va.), gave her, among other things, a gold and diamond chip cuff. They were divorced in 1982.

Taylor called Warner earlier this week to tell him of her engagement, his press secretary, Peter Loomis, said. "They remain good friends. I hear she looks wonderful. He wishes her all the best. But if he's going to the wedding he hasn't told me. I don't think he knows Stein."

Chen Sam, Taylor's spokeswoman, yesterday confirmed the engagement but gave no wedding date. The couple were introduced by theater executive James Nederlander at the Breeder's Cup races at Hollywood Park in Los Angeles about a month ago. Taylor, whose first famous movie was "National Velvet," is a great lover of horses. Stein has been described as a man-about-Manhattan.

Stein plans to join Taylor's children at a family house party in her chalet in Gstaad, Switzerland, at Christmas.

The Pritikin Longevity Institute, where Stein is said to have been getting in shape, said, "Mr. Stein checked out some time ago." A year ago Taylor underwent treatment for drug and alcohol addiction at the Betty Ford Center at Eisenhower Medical Center at Rancho Mirage, Calif. The legendary brunet beauty emerged thinner and with blond hair.

Currently Taylor is in Los Angeles filming a CBS Television comedy-drama, "Malice in Wonderland," in which she plays gossip columnist Louella Parsons. The filming is expected to be completed on Dec. 21, and it will be shown in the spring, Sam said.

Stein, friends say, has been married only once, briefly. Taylor married Warner in 1976, actor Richard Burton in 1964 and 1975, singer Eddie Fisher in 1959, movie magnate Mike Todd in 1957, actor Michael Wilding in 1952 and hotel heir Nicky Hilton in 1950. She was engaged for several months recently to Victor Gonzalez Luna, a Mexican lawyer, but that was broken off. More recently, she has been seen with Carl Bernstein, the journalist.

Meanwhile, Dennis L. Stein, a 29-year-old Manhattan tax lawyer with Bruns Summit, has been receiving calls congratulating him on his engagement to Taylor. Stein, who is perfectly happy with his six-year arrangement with another woman, says, "I've decided to say, 'Thank you, send the wedding presents here.' My lady friend says she'll take the diamonds."