As a youngster in Washington, Gore Vidal read political articles aloud to his blind grandfather, Oklahoma's Sen. Albert Gore, and as Gore's Senate page, he escorted him around Capitol Hill. Today, 56-year-old Vidal --screen writer, professional talk-show guest and author of such books as Myra Breckinridge, 1789, Burr and Creation --wants to be the junior senator from California for a single term.

"I'm in a very curious situation," says Vidal. "I'm highly political, always have been. I'm able to use television and print in order to express myself, and yet I'm in no position to get anything done. To somebody with an activist nature like mine, even a belligerent nature, this is extremely frustrating."

So after a year-and-a-half of lecturing in about 200 California towns, Vidal announced he would challenge Jerry Brown for the Democratic nomination for S. I. Hayakawa's Senate seat. Appearing on Johnny Carson's "Tonight Show" before his March announcement, Vidal confessed that the urge to run against "our Zen Buddhist Jesuit governor, the lord of the Medflies" was becoming "irresistible." He said he felt "kind of humble to think I might be taking the place of Hayakawa--who has given Valium a bad name--in an office once held by George Murphy and John Tunney, who had the most beautiful teeth I've ever seen."

Vidal's wit promises to enliven a race in which he knows he is the underdog, compared with Brown, when it comes to money and organization. He's betting on his recognizability and Brown's unpopularity to help him win the June 8 primary. Should he triumph in the general election, Vidal and New York's Sen. Daniel Patrick Moynihan (presuming he wins reelection) could vie for the title of Capitol Hill's foremost orator.

In 1960, Vidal was an unsuccessful Democratic candidate for the House from New York. And along with Benjamin Spock, he co-chaired the "People's Party" between 1968 and 1972. Sitting in the living room of the grand stucco home he refurbished in Los Angeles, Vidal chatted recently about his latest bid for office.

* On the seduction of power and Washington infighting: "The long knives can't touch you when you don't want anything. What do I want? I don't want any more publicity, glory or money. So when you start out with that, you're almost invulnerable."

* On his wit: "There's only one danger in it, in that it overexcites the print media. They will first try to be cleverer than I, and they may very well succeed, which means we're both in trouble. Or they will simply do one- liners and leave out anything of substance. So there is a point that I've got to slightly cool it."

* On serving a single term: "I take the view which I ascribe to the Founding Fathers, who, after all, were not always entirely wrong. They thought that, particularly in the Senate, after you've achieved your fame and fortune, you then went to Washington and gave six years of your life and went home. I like that idea. I certainly don't like the idea of some kid going straight from law school to Congress and running and running and running. That's the problem with Brown. He's had something like eight campaigns in 10 years--this is very bad for your character."

* On his main campaign issue: "I have a particular target: the military budget. We will either go bankrupt or engage ourselves in nuclear war if Mr. Reagan gets what he wants for the Defense Department. There is the root of all of our problems. Or put another way, no problem can be solved as long as something like that continues."

* On raising money: "I really started late. I'd not taken into account the extent of the Depression's effect on people giving money and the fact that . . . you can't go to Beverly Hills without stumbling over some itinerant senator from Michigan trying to raise money. These carpetbaggers are driving everyone crazy around here."

* On his bad-boy reputation fueled by past advocacy of bisexuality and risqu,e writings: "I'm a fact, something people see. Do you realize that most people under 45 have seen me all their lives? I'm part of the national furniture . . . The problem with journalism is that it's essentially threading clich,es . . . If you have a figure who does not conform to anything you're used to, then you have to say 'outrageous!' and so on . . . I'm prepared for that. Anyone who is a critic of this society is not going to have a terribly good press. But he may have an enormous audience."

* On his favorite senators: "I like (Alan) Cranston (California's senior senator). As professional senators go, he's one of the best, but professional, as you might gather, is not my idea of an amiable adjective. Of the others, I can't think of one offhand who strikes me as being particularly distinguished."

With comments like that, Vidal won't win many friends in official Washington. And with his proposals to tax corporations a flat 10 to 15 percent on their gross adjusted income, he need not look for corporate political action groups to contribute to his race. Instead, he's relying on some 1,000 volunteers whose names he collected during his 18 months of speaking around the state to push his candidacy. A former California Democratic state party chairman signed on to run the Vidal campaign, and Democratic money angel Max Palevsky is his finance chairman. If he wins, will he be a shy freshman?

"I wouldn't worry about the shyness," vows Vidal. "Whatever you worry about, don't worry about that. They will know I'm there."