Frazier was first elected to the Allegheny County Council for District 13 in 2001, taking over the two year remainder of Tom Foerster's term in office. She ran as a Democrat but was not endorsed by the party, likely due to her connections with Republican Jim Roddey, who was serving as the county's chief executive. Frazier had been appointed by Roddey to his transition team. She received 4,735 votes in the Democratic primary on May 15, 2001, beating Robert Biel with 3,955 votes, Richard Stahl with 3,058 votes, Vernon L. Boozer with 828 votes, and Daniel Styche with 453 votes. She was the first Black woman elected to the county council following its establishment as a home-rule government the year prior and one of three members of the fifteen-person council who was not a white man. Frazier served as chair of the organization that she founded, the Allegheny County Black Elected Officials. She chaired the health and human services committee and was a member of the appointment review, budget and finance, economic development, government relations, and campaign reforms committees.
