The fifth of twelve children born to a prominent Shreveport businessman, Alexander was educated in private elementary and secondary schools. He received his Bachelor of Arts degree from Louisiana State University in Shreveport. He obtained his law degree from Oklahoma City University School of Law where he served on Law Review and Moot Court, both intramural and on the Benton National Moot Court Team. He was a law clerk to Judge Rebecca F. Doherty of the U.S. District Court for the Western District of Louisiana. An appointee of former U.S. President George H.W. Bush, Doherty is based in Lafayette and Opelousas. Himself a former administrative law judge, Alexander has also been in private practice, handling both criminal and civil cases. Alexander was chief of staff to former U.S. Representative Rodney Alexander of Louisiana's 5th congressional district. The two are unrelated. In 2006, the Democrats in Washington, D.C., accused Royal Alexander and several others, including members of Congress, of having acted too slowly regarding the disclosure of the name of the congressional page who was sent inappropriate email messages by then U.S. Representative Mark Foley of Florida. Evidence showed that Royal Alexander reported the inappropriate email messages to the staff of House leadership upon his learning of the information. The matter quickly died after the 2006 congressional election, in which Democrats gained control of both houses of Congress. Alexander was a staff member to the late U.S. Representative Clyde C. Holloway of Louisiana's 8th congressional district, since disbanded, who also served as chairman of the Louisiana Public Service Commission
Race for attorney general
A first-time candidate for public office in 2007, Alexander finished second to James D. "Buddy" Caldwell, then a Democrat, in the nonpartisan blanket primary for state attorney general. Alexander outpolled incumbent Democrat Charles Foti of New Orleans for the right to enter the general election against Caldwell, a five-term district attorney from Tallulah in northeast Louisiana. Caldwell received 477,574 votes; Alexander 395,645 votes. Foti finished with 389,658. With only four weeks between the primary and the general election, the traditional Democratic political machine of sheriffs and district attorneys flocked to fellow Democrat Caldwell. Alexander was defeated in the second round of balloting when Foti's base switched to Caldwell. In 2011, Caldwell switched his affiliation to the Republican Party and won a second term but was defeated in 2015 by Republican Jeff Landry. Alexander's primary strength was demonstrated in Shreveport, Alexandria, and Monroe.
Caddo Parish assessor candidacy
Alexander was the unsuccessful Republican candidate in the October 22, 2011, primary for Caddo Parish tax assessor. He polled 16,255 votes, while the incumbent Democrat, Charles Russell Henington, Jr., received 30,310 votes. Henington last faced opposition in 1999, when he won the assessor's position by defeating an earlier Republican candidate, John W. Wessler, by a five-to-one margin. Henington's father, Charles Henington, Sr., and his step-grandfather, Albert Galloway Hammett, Sr., previously served as the Caddo Parish assessor, having kept that office within the reach of one family for, through 2011, seventy-eight years. A. G. Hammett was the assessor from 1933 to 1964. According to KTBS-TV, ABC in Shreveport, an independent survey of property tax rates around the state by the demographerElliott Stonecipher concludes that Shreveport and Caddo Parish residents pay the highest such taxes of any metropolitan area in Louisiana. Alexander said that the assessments are inflated and had pledged had he been elected to reduce them. Alexander also accused Henington of not informing senior citizens that they retain the option of freezing their property taxes once they reach the age of sixty-five.
Civic activities
Royal Alexander remains active in public life. He is a frequent lecturer to various civic and educational organizations regarding the United States Constitution. He also serves as an occasional media guest giving analysis on current political and social issues as they relate to the United States Constitution.