Every branch has snipers per say, even the Army National Guard. There isn't any AFSC (Air Force), MOS (Army) or Rating (Navy & Coast Guard) for "sniper." Sniper is an "additional skill" that is held by members in addition to the normal duties of their AFSC/MOS/Rating.
In the vast majority of cases (especially in the Army, and Guard) snipers hold the MOS of "Infantry." They perform sniper duties when required, and when not performing sniper duties, they perform as part of an Infantry unit. In the Navy and Air Force, they perform as part of a "ground combat unit" (Security Forces in the Air Force, and SEALS or Shore Patrol in the Navy).
Below is some stuff I pulled from the net.......
Scout Sniper, (MOS 0317, formerly 8541) is a specialist in the United States Marine Corps whose mission is to deny the enemy freedom of movement by neutralizing enemy leaders, crew-served weapons operators, radiomen, observers, messengers, and other key personnel with single, well-aimed shots. In addition, scout snipers also provide close reconnaissance and surveillance to the infantry battalion. Scout Snipers attached to Marine infantry battalions fall under the Surveillance and Target Acquisition units, usually a reduced platoon with the headquarters company.
Scout/Sniper also refers to a member of a U.S. Army Reconnaissance platoon's sniper section; though unlike the Marine position, this is not a designated MOS but rather a position denoted on the individual unit's MTOE. Scout/Snipers are typically found in the Recon platoon of the infantry Headquarters and Headquarters Company (HHC), or interspersed into Reconnaissance, Surveillance, Target Acquisition (RSTA) squadrons and troops.