Sen. Alan Cranston stalked the marbled halls of the state capitol here today to hustle young Democratic activists at a state convention and fuel the notion that a Californian running for president can generate support in the Cradle of the Confederacy.

Cranston has thrown down the gauntlet in Alabama, the linchpin state in his southern strategy. He has organized hard, visiting half a dozen times since last year, twice meeting with Gov. George C. Wallace, and lobbying teachers, blacks and labor as well as the young party workers who soldier campaigns.

He won a straw poll of presidential candidates at the annual convention of 124 Alabama Young Democrats today, but even top campaign aides said it tested his strong state organization more than his appeal to a conservative electorate.

He got 53 percent of the vote from members of Democratic clubs who came to Montgomery to press the flesh, drink free wine and beer aboard a Cranston riverboat cruise and vote in a pretend primary. Sen. Ernest F. Hollings of South Carolina was second with 15 percent, followed by Gerald Willis, former state legislator and wealthy lumberman, with 11 percent, and former vice president Walter F. Mondale and Sen. John Glenn of Ohio with 7 percent each.

Cranston said he was "disappointed" at the turnout, having anticipated upward of 300 young Democrats. But he said that his 65 straw ballot voters would be "the basis of my campaign in Alabama."

The straw poll "will give us the opportunity to go into other southern states and show others who want to join Alan Cranston that they're not wasting their time," said Sergio Bendixen, the senator's campaign manager.

On the other hand, "No one shoud take us very seriously in the straw poll because we don't represent the grass roots," said Joe Macon, 34, a lawyer from Elmore County who abstained from voting.

As the candidate of the straw poll, Cranston beat Mondale in Wisconsin last week, won another test in California and placed second in Massachusetts to much surprise. The South was the only region of the country where he had yet to demonstrate support.

So he played his cards in Alabama, which like Georgia and Florida has a primary on March 13, "Super Tuesday" down South. If his nuclear freeze candidacy can find a home in Alabama, Cranston figures he can win delegates across Dixie.

Gov. Wallace yesterday welcomed Cranston to the mansion, telling him he favors "both the United States and the Soviet Union not only freezing nuclear weapons but reducing them." But Wallace added that he opposes a unilateral freeze and favors building enough nuclear weapons to defend the country until a mutual freeze can be worked out.

Said Cranston: "Gov. Wallace has stated my position on the freeze exactly."

To dispel a "California" image that conjures such Bible Belt horrors as long hair, hot tubs and bacchanal, the senator salts speeches with reminders of his votes for a strong defense and for cuts in capital gains taxes to fuel investment.

"He's not all that California crazy," said Carolyn Morris, 26, a pre-law student at the University of Alabama in Birmingham who sported a Cranston button. "What he says makes sense. If we keep heading where we're heading, we'll destroy ourselves."

She is among more than 100 new members of the Birmingham YDs recruited by Cranston workers since the straw poll was announced in April as a gimmick to boost membership.

Cranston plans to use Alabama as the launching pad to run in primaries or caucuses in nine more southern states, said Bendixen. He chose Alabama over the other early primary states because in Florida Reubin Askew was once governor and in Georgia Mondale enjoys a Jimmy Carter connection.