Vietnam Medal of Honor Recipient. He served during the Vietnam War in the United States Marine Corps as a Private First Class (PFC) with the 3rd Reconnaissance Battalion, 3rd Marine Division (Rein), FMF. He was awarded the MOH for his bravery at Fire Support Base Argonne, Republic of Vietnam on March 5, 1969. His citation reads "For conspicuous gallantry and intrepidity at the risk of his life above and beyond the call of duty while serving as a Machine Gunner with Company C, 3rd Reconnaissance Battalion, in connection with operations against enemy forces. Early in the morning PFC Jenkins' 12-man reconnaissance team was occupying a defensive position at Fire Support Base Argonne south of the Demilitarized Zone. Suddenly, the Marines were assaulted by a North Vietnamese Army platoon employing mortars, automatic weapons, and hand grenades. Reacting instantly, PfC Jenkins and another Marine quickly moved into a 2-man fighting emplacement as they boldly delivered accurate machine gun fire against the enemy. A North Vietnamese soldier threw a hand grenade into the friendly emplacement. Fully realizing the inevitable results of his actions, PFC Jenkins quickly seized his comrade, and pushing the man to the ground, he leaped on top of the Marine to shield him from the explosion. Absorbing the full impact of the detonation, PFC Jenkins was seriously injured and subsequently succumbed to his wounds. His courage, inspiring valor and selfless devotion to duty saved a fellow Marine from serious injury or possible death and upheld the highest traditions of the Marine Corps and the U.S. Naval Service. He gallantly gave his life for his country." His Medal was awarded to his family by Vice-President Spiro T. Agnew at the White House on March 5, 1969.

A 149-bed home for elderly veterans in Lake City, Florida was named in honor of PFC Jenkins, specifically the "Robert H. Jenkins, Jr. Veterans Domiciliary Home of Florida." Additionally, Robert H. Jenkins, Jr. Elementary School in his hometown of Interlachen, Putnam County, Florida, is also named after PFC Jenkins.

His name is found on Panel 30W, Line 046 of the Vietnam Memorial Wall in Washington, DC.