After graduating from Columbia's Law School in 1946, Baker was hired by the NAACP Legal Defense and Educational Fund (LDF) as a civil rights lawyer. As the fund's first female attorney, she became Associate Counsel to the LDF, making her a lead trial attorney in a number of early and significant civil rights cases including representing Martin Luther King Jr., the Freedom Riders, and the Birmingham Children Marchers. Baker visited churches that were fire bombed, sang freedom songs, and visited Rev. Martin Luther King Jr. while he sat in jail, as well as spending a night with civil rights activist Medgar Evers under armed guard.