Yes, Indian army uses sniper rifles.
the major lot of the rifles include the locally made dragunov svd 7.62X54R called the dv59 variant.
this forms a common lot among the infantry men as it is a designated 'marskmen' rifle.
also we do use mauser sp66 (basically a hunting rifle) bolt action rifle.(7.62X51)
other highend sniper weapon systems our army uses are the hk-psg1, hk-msg 90.
also our army uses high caliber rifles (anti material rifles) we use Mechnev ntw-20 anti mateiral rifle. This rifle is highly modular, and comes with a wide choice of ammo and barrel selection.(14mm- 20mm) as per mission demands. also different types of rounds can be used starting from conventional rounds to armour piercing, to incendiary. many of us have a perception that the barret is the best but there are a lot of other players that too are far better than the barett(tv propoganda and all, no doubt barett is a good weapon but still there are others to consider) this weapon system is mainly used by our special forces. unlike the western counterparts where there is a lot of talk about snipers and other hardware, here in india it is not that much in to use as we dont have such utility except in few cases. And yes, all our special forces guys are no doubt the bestest shooters as their passing criteria is min. 80% shooting targets accurately under most adverse conditions.
our jawans have a better eyesight. the simple example is that they can shoot down the target upto a decent range with open iron sights unlike the others we see in movies that are equipped with laser sights.
i am writing this as i have seen these anti material gun at 'know your army' exhibition way back in my college days when i was battalion commander of ncc(fortunate that i could click fotos) i would love to share lots of fotos of military exhibition but sadly i dont know how????