California Republicans anticipating an easy reelection next year for Gov. George Deukmejian today found their man trailing prospective Democratic challenger Tom Bradley, mayor of Los Angeles, in a new statewide poll.

Mervin Field, whose California Poll shows Bradley leading Deukmejian 50 percent to 44 percent, said he was equally surprised to find the governor behind despite "a trend toward Republicans" and the state's "good financial shape."

Field noted that both men received very favorable ratings from the 809 voters polled: 81 percent for Bradley, 70 percent for Deukmejian. The difference appeared to be less a slap at Deukmejian than a compliment to Bradley, who successfully staged the 1984 Olympics here and was overwhelmingly elected to a record fourth term.

Deukmejian narrowly defeated Bradley for the governorship in 1982 after intense opposition to a gun-control initiative on the ballot brought in thousands of unexpected Republican absentee ballots. Some younger Democrats have tried to discourage Bradley, 67, from running for governor again, but the poll results make a rematch more likely.

"Obviously we were very encouraged" by the poll, said Tom Houston, Bradley's deputy mayor. "George Deukmejian is a lackluster performer who doesn't provide the dynamic leadership Californians deserve."

Questioned by reporters today in Ione, Calif., during an early campaign trip, Deukmejian, 57, said, "I always seem to start out in the polls as an underdog, and that is not a very bad position to be in . . . . "

Field said three recent private polls, two for Republicans and one for Democrats, also revealed a preference for Bradley. Field's poll was taken early this month, before controversy arose over the mayor's statement Monday that poor preschool children in Watts should be placed in motivational programs "away from their parents, because that's what it's going to take . . . to give them direction and training."

At a news conference Thursday Bradley, who is black, said he did not mean that children should be physically taken away from their parents and said any such program should be voluntary.