Rutherford, who was elected to the board in November 2010, succeeds Supervisor Josie Gonzales as board chairwoman.
Rutherford said in a statement Tuesday that the board has made "tremendous strides" over the past two years to focus on the County Vision to restore public faith in government.
"I pledge to continue those efforts with the help and support of my colleagues on the Board of Supervisors," Rutherford said.
The County Vision is a 20-year action plan drafted to address quality-of-life issues county residents deemed most important in a survey.
Supervisor Gary Ovitt was appointed vice chairman at Tuesday's meeting - the first of 2013.
The role of chairperson is a vital part of making policy that affects the entire county, Gonzales said.
In that role, Rutherford will become the leadership face of the board, and she will speak on behalf of the supervisors and the county.
Gonzales called the role an "awesome" responsibility after her colleagues appointed her two years ago.
"It's a daunting responsibility," she said. "The gravity of the responsibility has never left me."
The county charter requires the board to elect a chair at the first meeting in January after an election of supervisors.
Rutherford will have a challenging path ahead, Gonzales said.
In Gonzales' term, she had her own tough road, including efforts to reconstruct the county's image after high-profile corruption scandals.
Among those reconstruction efforts, Gonzales refused compensation for her chairmanship.
Rutherford will have her own unique challenges, Gonzales said.
Among them: leading the board through rough budgetary waters and setting the board's agenda through a still- fragile economy.
"There will be some challenges," she said. "No way the road will be smooth ahead."
Staff writer Ryan Carter contributed to this story.
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