As the only FBI field agent in Washington, D.C., fluent in Spanish in 1954, Rudd participated in the interrogation of the Puerto Rican nationalists involved in the attack on the US House of Representatives that year.

His report impressed Director J. Edgar Hoover, who offered Rudd his next choice of assignment, which he received as U.S. legal attaché at the U.S. Embassy in Mexico City, where he served from 1960 to 1970.

Rudd obtained Oswald's file from the Mexican government and flew a Cessna aircraft from Mexico City to Dallas, Texas, to provide the documents to FBI officials in Dallas as Kennedy's body was on its way to Washington, D.C., with Vice President Lyndon B. Johnson and widow Jacqueline Kennedy.

Four years later, he won election to the House of Representatives for Arizona's 4th congressional district, which then comprised the entire northeastern portion of the state.

Rudd was a fiscal conservative, and a member of the important Appropriations Committee for five years; he opposed the expenditure of federal taxpayer dollars for abortions.