Born at Coles Creek, Mississippi, Davidson completed preparatory studies before going on to study law. He was admitted to the bar and commenced practice in Greensburg, Louisiana. After this he was appointed register of the United States land office. He served as member of the Louisiana House of Representatives from 1833–1846.
Davidson was elected as a Democrat to the 34th, 35th, and 36th Congresses (March 4, 1855 – March 3, 1861). After his time in congress he resumed the practice of his profession. He served as president of the Democratic State convention in Louisiana in 1855. He served again in the Louisiana House of Representatives 1874—1878, 1880, and 1883.
He died in Springfield, Livingston Parish, Louisiana, September 11, 1883. He was interred in Springfield Cemetery.