The Pan American Round Table was begun by Mrs. Florence Terry Griswold in 1916. Believing that women could develop an understanding that men, with their involvement in commerce and politics, could not, she opened her home to refugees from the Mexican Revolution,qv and enlisted friends to aid them as well. On October 16, 1916, she assembled a group of women at a luncheon at the Menger Hotelqv in San Antonio, where they organized the Pan American Round Table, "to provide mutual knowledge and understanding and friendship among the peoples of the Western Hemisphere, and to foster all movements affecting the women and children of the Americas." Among the founders were Mrs. A. C. Pancoast, Mrs. Eli Hertzberg, Mrs. Joseph Burton Dibrell, and Mrs. Carlos Bee. Mrs. Griswold chose the medieval round table as a symbol of unity, perpetuity, equal representation, and opportunity. The founders selected a variation of the motto of the Three Musketeers: "One for all and all for one." Mrs. Griswold became the first director general, adopting the official title used by the head of the Pan American Union. She also followed that organization's policy in prescribing that each member of the Round Table represent one of the twenty-one American republics. The Pan American Union's principle that only through education and communication, not legislation, can understanding and friendship grow, formed a basis for the Round Table; indeed, cooperation with the Union and its policies enabled Mrs. Griswold to build a firmly knit organization. As this movement grew, other tables were organized throughout Texas. Laredo became the second in 1921, followed by El Paso that same year and Austin in 1922. The first Latin Table was organized in Mexico City in 1928; the first outside the United States or Mexico was begun in Costa Rica in 1936. By 1944 enough chapters had been formed throughout the United States and Latin America that an international body, the Alliance of Pan American Round Tables, was founded in Mexico City.

In 1992 twenty-four Round Tables met in Texas, with a membership total of 1,400. Other United States Tables are in California, Illinois, New Mexico, Oklahoma, and Washington, D.C. There were 124 Tables of the Alliance of Pan American Round Tables in fifteen countries in Latin America. In Texas the Tables are nearly autonomous, each with its own constitution. The state organization came into being as a communication center rather than as a governing board. State conventions are held in odd-numbered years; alliance conventions are held in even-numbered years. Pan American Day, established by presidential proclamation on April 14, 1931, is observed wherever a Pan American Round Table exists.