President Carter has moved into a clear lead in the South after trailing his Republican rival, Ronald Reagan, in that region before the Democratic National Convention, according to a new Gallup Poll.

The poll, completed last Sunday, shows Carter as the choice of 48 percent of registered voters in the South, compared to 39 percent for Reagan and 8 percent for independent candidate John B. Anderson. In a survey done before the Democratic convention, Reagan led Carter 44 percent to 36 percent in the South, with 9 percent for Anderson.

The most recent survey shows Carter and Reagan running even nationwide -- Reagan has 39 percent, Carter 38 percent and Anderson 14 percent.

The president has scored gains outside the South, but not enough to overtake Reagan. The preconvention survey showed Reagan with 45 percent support beyond the South, Carter with 29 percent and Anderson with 16 percent. The postconvention results show Reagan with 39 percent, Carter with 35 percent and Anderson with 16 percent.

The survey indicates that Anderson's candidacy is more damaging to Carter than to Reagan. When Anderson's name is included in the survey, he draws 8 percent of his vote from Carter and only 1 percent from Reagan.

A comparison of the pre- and postconvention surveys also indicates that Democratic voters have shifted back to Carter in large numbers. While only half of Democrats chose Carter in a test against Reagan and Anderson in the preconvention survey, 62 percent now do so.