Linthicum was born near Baltimore, Maryland, in the locality now known as Linthicum Heights, Maryland, and attended the public schools of Anne Arundel County and Baltimore. He graduated from the State normal school in Baltimore in 1886, and became principal of the Braddock School in Frederick County, Maryland in 1887. He also taught in the schools of Anne Arundel County, and studied history and political science at Johns Hopkins University in Baltimore. He graduated from the law department of the University of Maryland at Baltimore in 1890, and was admitted to the bar and commenced practice in Baltimore in 1890.

Linthicum served as a member of the Maryland House of Delegates in 1904 and 1905, and in the Maryland State Senate from 1906 to 1909. He was an unsuccessful candidate for mayor of Baltimore in 1907, and was a judge advocate general on the staff of Maryland Governor Austin Lane Crothers from 1908 to 1912. He was elected as a Democrat to the Sixty-second and to the ten succeeding Congresses and served from March 4, 1911, until his death. During the Seventy-second Congress, he served as chairman of the U.S. House Committee on Foreign Affairs, and had been renominated to the Seventy-third Congress at the time of his death. Linthicum had also served as delegate to the Democratic National Convention in 1924. He died in Baltimore, and is interred in Druid Ridge Cemetery.