I would think the Brutes would adopt a more brutal, crude, medieval kind of weapon. Take a look at all of their weapon or weapon variants. Your suggestion is too much like the UNSC Rail Gun and not Brutish enough, need something different. The "Bow" is a good idea though, for it is an old style weapon, one perhaps the Brutes could be fond of. If the projectile is similar to a giant arrow (or black arrow from LOTR, used to damage ancient Dragons) it would be very cool. Thing is, a bow is kinda not the style of a Brute. Sit back and snipe? No no, a Brute wants to be in on the action, taste the blood and smell the fear secreted by their enemies.
Brute Shot: Has a sharp, curved blade for a powerful melee. Simple explosive grenades as well.
Gravity Hammer: An enhanced hammer. Pure futuristic melee weapon. The "gravity" addition makes sense with a hammer...something that inflicts damage with kinetic energy powered by muscle would benefit from some tech buffs. In this instance, additional gravity/force/anti-gravity tech.
Spiker: Perhaps a nod to prehistoric/pre-Covenant Brute weapondry, this weapon is crude by intention. Propels giant, super-heated spikes to pierce, burn, and impale targets. An ideal Brute weapon, fundamentally.
Brute Plasma Rifle: Perhaps the least Brute of any known Brute affiliated weapon. It fires faster and thus overbears the tech faster, a nod to the Brute's impatience and lust for violence at the cost of weapon efficiency. Also can be seen as an argumentative move against the Elites. Brutes taking their place in the Covenant, and changing/defacing the Elite's weapons.
If the Brutes were to have a Sniper weapon, it would have to have a crude edge to it. A weapon like the Railgun wouldn't fit because it is simply too much like UNSC and their preferred tech. Sleek, fast, efficient, futuristic. The Brutes would use a more brutal weapon, with simpler tech that can inflict gruesome, or perhaps gory, injuries.
All in all, I do not think a sniper weapon would fit the Brutes. Maybe a mid-range weapon, but not a sniping.