Republican presidential candidate John B. Connally, who has picked the March 8 South Carolina primary as the place to make his stand against Ronald Reagan, has picked up the support of the state's two leading Republicans.

Sen. Strom Thurmond and former governor James B. Edwards, who both backed Reagan in his 1976 race against then-President Ford, are expected to announce their endorsements at a series of new conferences in South Carolina today.

Their support could be a significant boost for Connally, who trails Reagan in public opinion polls in South Carolina and who is behind Reagan and George Bush in the key early states of Iowa and New Hampshire.

"It's going to make it a real horse race," said Harry Dent, a South Carolina lawyer who was an architect of former president Richard Nixon's 1968 victory and who later worked in the Nixon White House. "It wasn't a horse race previously." Dent, a longtime Thurmond associate, said he himself is neutral in the race.

Connally's campaign strategy is now keyed to stopping Reagan somewhere in the South, and he has picked South Carolina for heavy campaigning in part because its primary comes three days before those in Florida, Georgia and Alabama.

Thurmond and Edwards could prove crucial to Connally because of their support among Republicans in South Carolina. "It's the combination of Edwards and Thurmond that makes it so po tent," one South Carolina political expert said. "Each reinforces the other."

He described Thurmond as "as potent a figure with hard-core southern Republicans as there is," and said the senator's endorsement could spill over into other southern states.

Connally campaign officials are counting on Thurmond and Edwards to campaign actively in the state for the former Texas governor. Both are extremely popular with the Republican rank and file, and Thurmond's organization goes beyond party lines. Because the March 8 Republican primary is open to all voters, Thurmond's endorsement could help Connally attract conservative Democrats and independents.

Although Edwards supported Reagan in 1976, he was upset over Reagan's choice of Sen. Richard S. Schweiker (R-Pa.) as his running mate. Edwards apparently is still at odds with John Sears, Reagan's powerful campaign manager. His decision to back Connally also may have been affected by the fact that his chief rival for control of the state Republican Party, Rep. Carroll Campbell, is running Reagan's campaign in the state. Edwards, who has been leaning to Connally in recent weeks, also worked for Reagan in 1968.

In contrast, Thurmond was the key to stopping Reagan in the South in 1968 when he backed Nixon, a move that guaranteed Nixon's nomination. But in 1976 Thurmond endorsed Reagan against Gerald Ford.

Reagan campaign officials had feared that Edwards would endorse Connally before Reagan could get organized in the state, and now believe his support will not make much difference.

The South Carolina primary is seen as a two-person race at this point, but the field also will include Sen. Howard H. Baker Jr., who is hoping to capitalize on his roots in nearby Tennessee.