She was the youngest of three daughters. Her father, Presciliano Martinez Rangel, from Duval County, was orphaned at an early age and was able to attend school for only one year. Her mother, Herminia Lerma, moved with her parents from Starr County to Kingsville. Presciliano worked in farming, ranching, construction, and business. He became a merchant and owned an appliance store, a furniture store, a plumbing service, two barber shops, and a bar. He helped his wife build a successful dress shop located just off the main street of Kingsville, not restricted to the "Mexican side" of town.
In 1947, when Rangel was a teenager, her parents were able to buy some land near Texas College of Arts and Industries and hoped to build a home. But the land was in the "Anglo-white" district and the neighbors organized against allowing a "Mexican" family to build in their neighborhood. Ultimately, the family was allowed to design and build the Spanish Colonial style house across from the college campus that Rangel called home until her dying day. Rangel and her sisters grew up in Kingsville, attending the Mexican Ward School for the elementary grades, and the town's only integrated high school.
Rangel and her oldest sister decided to attend the Texas College of Arts and Industries, now Texas A&M University–Kingsville. After graduating with degrees in education, Rangel began teaching in the neighboring community of Robstown. Then she and her oldest sister, Olga, decided to become teachers in an overseas program in Venezuela. This determination to be of service to society and fight for good causes impelled Rangel to return to Texas and attend St. Mary's University Law School. She went on to become one of the first Hispanic female law clerks. After her clerkship with U.S. District Judge Adrian Spears, she became one of the first Hispanic women assistant district attorneys in Texas by working in the District Attorney's office in Nueces County. She returned to Kingsville, where she opened her own law practice and was the only Hispanic woman attorney in the city.
In 1974, Rangel began her life in politics by running for, and winning, the chairmanship of the Kleberg County Democratic Party. But she had more ambitious goals and decided to run for a seat in the Texas House of Representatives. She gathered her girlhood friends, family, and a few newcomers to Kingsville and worked hard to win the seat that would make her the only Hispanic woman in the legislature. In 1993, she closed her successful law practice in order to serve her district as a legislator full-time. Upon her death on March 17, 2003, the Mexican American Legislative Caucus of the Texas House issued a news release, which summarized her legislative career.
In 1993, she secured $460 million for the South Texas Border Initiative. In the last legislative session, Representative Rangel passed a bill creating the first professional school in South Texas — Texas A&M Health Science Center - Irma Lerma Rangel College of Pharmacy. In 1995, Speaker Pete Laney appointed Rangel Chair of the Texas House Committee on Higher Education.
As the first Mexican-American to head the committee, Rangel led the charge to ensure educational opportunities for all children. Rangel joint-authored and sponsored legislation creating the TEXAS Grant I and Grant II Programs, which have allocated millions of dollars in financial support to low-income students. In response to the Hopwood v. Texas decision, which ended affirmative action at all state colleges and universities, Rangel pioneered landmark legislation in 1997 (House Bill 588) which requires state colleges and universities to admit automatically all students who graduate in the top 10 percent of their high school class.