During his adolescence, he attended the public schools in Manati while working at a drugstore owned by another cousin, Clemente Ramírez de Arellano Córdova.

After the United States acquired Puerto Rico in 1898, Córdova Dávila, knowing very little English, decided to invest the earnings of a book of poetry that he produced to attend law school in Washington, D.C.

Attracted by low tuition costs, he enrolled at Howard University Law School, not aware of it being a black college.

On January 12, 1912, Córdova was one of nine attorneys and judges who founded Puerto Rico's first law school under US rule, operating out of the Ateneo Puertorriqueño, serving as its first Civil Code professor.

On July 16, 1917, Córdova Dávila was elected as the Union Party candidate to serve as Resident Commissioner from Puerto Rico to the United States, succeeding Luis Muñoz Rivera, who had died the preceding November and had recommended him as his successor.

The Resident Commissioner, on the other hand, wrote to his friend Epifanio Fernández Vanga, that Muñoz Marín "has natural talent but lacks the education to perform at this task...everything was disorganized...and my office's image was being affected".

On April 11, 1932, Córdova Dávila resigned as Resident Commissioner after having been appointed by President Herbert Hoover as an associate justice of the Supreme Court of Puerto Rico.