Jordan was born in Pine Bluff, Jefferson County in southern Arkansas, to Mr. and Mrs. J. Lomax Jordan, Sr. He graduated from Lafayette High School in 1970 and the University of Louisiana at Lafayette (then the University of Southwestern Louisiana) in 1974. He was listed in Who's Who in American Colleges and Universities. Thereafter, he procured his law degree from Louisiana State University Law Center in Baton Rouge. He worked in various research positions for both the State Senate and the Louisiana Legislative Council in the latter 1970s, prior to the establishment of his law firm in 1979. Jordan was an assistant district attorney from 1981–1982. In his private practice, he specializes in Personal Injury and Accident cases and Criminal Defense Law.
Jordan unseated Democratic state Senator Allen Ray Bares (1936-2008); pronounced BAH REZ) in the 1991 general election. Bares had been first elected to the Senate in 1979, when he was challenged by among others, the equally prolife William Dudley "Dud" Lastrapes, Jr., later the conservative Republican mayor of Lafayette. Bares, who also served in the state House from 1972-1980, won again in 1983 and 1987.
In 1991, Bares authored a controversial measure which would have outlawed most abortions in Louisiana. The legislature approved the bill, but it was vetoed by Democrat-turned Republican Governor Charles Elson "Buddy" Roemer, III, on the grounds that it went beyond the scope of the United States Supreme Court decision Roe v. Wade. Feminist groups such as the National Organization for Women, subsequently headed by the Louisiana native Kim Gandy, formerly of Bossier City, targeted Bares and a prolife House member, Democrat Carl Newton Gunter, Jr., of Rapides Parish for defeat. The controversy worked to Jordan's advantage though he too took the prolife position. In the end, Bares and Gunter were defeated in what Louisiana feminists hailed as a great success.
Bares led in the primary with 13,409 votes (40 percent), but Jordan ran second with 9,313 (28 percent). Two other Republicans, Carl W. Tritschler (born February 16, 1964) and Max A. Menard received 6,713 (20 percent) and 3,921 (12 percent), respectively. The three Republican candidates, in what was otherwise a heavily Democratic year in Louisiana politics, polled a combined 60 percent in the state Senate primary. In the runoff, technically the general election on November 16, Jordan received 22,224 (60 percent) to Bares' 14,730 (again 40 percent).
Jordan won reelection outright in the 1995 primary. He received 20,629 votes (61 percent) to 10,823 (32 percent) for Democrat Sidney B. Flynn and 2,242 (7 percent) for "No Party" Charles Olivier.
In 1999, Michot, the son of a former state education superintendent, the businessman Louis J. Michot, also of Lafayette, roundly defeated Jordan. Michot received 25,699 ballots (68 percent) to Jordan's 12,347 (32 percent).
Jordan worked in the Lafayette City Court indigent defender program from 1979-1981. He has served on the Indigent Defender Board of Lafayette, Acadia, and Vermilion parishes. He has served on the board of the following youth-oriented groups: Lafayette Juvenile and Young Adult Program, Acadiana Youth, Inc., Pollux House, Lafayette Children's Shelter, and the Lafayette Community Correctional Center.