Try the single player mission "One Shot, One Kill"... (Assuming you have combined operations ?)... but be aware of the fact that you are shooting from a hill over a distance of roughly a kilometer and you need to compensate for bullet drop.
By the way, you might mix up sniper with marksman
Selct single player
Go into the Armoury.
Play a few missions. As you play you unlock weapons, vehicles and aircraft.
After a while you will unlock the various sniper rifles.
If you then select a sniper rifle you are given sniping missions.
If you select AT weapons you are given AT missions.