No, she is not. Therefore, she is not the first woman to run for President either. Both of those honors go to Victoria Woodhull who was nominated by the Equal Rights party in 1872. Twelve years later the same party ran Belva Lockwood and recieved 4, 149 popular votes across six states.
Hillary Clinton also is not the first woman to run for a major party’s nomination. That was Margaret Chase Smith who ran for Republican nomination in 1964 and 227, 007 votes in the primary. Mrs. Clinton isn’t even the first woman to run for Democratic party nomination. That was Shirley Chisholm in 1972 who was in the ballot in 12 states and got 152 delegates. In 1976 Ellen McCormack, running for Democratic nomination, was the first woman to qualify for matching funds.
Hillary Clinton is the first woman to win a presidential primary and the first woman to be nominated by a major party. If she wins the election she will become the first female President of the United States.