The primary sniper rifle used by the United States in World War II was the M1903A4 Springfield, a version of the exisiting 1903A3 with the iron sights removed and replaced with a Weaver 330C scope (adopted by the military as the M73B1). This was a low-power optic, but was centrally mounted on the rifle to avoid and of the windage issues caused by prismatic scopes.
The 1903A4 Springfield was the US’ first truly mass-produced sniper rifle, with more than 28,000 being manufactured during just two years of the war (1943-44). The rifle was taken out of production when the M1C sniper adaptation of the Garand was formally adopted, although production of the M1C would be delayed until the end of the war. The 1903A4 would remain in service after WWII, with later scopes being approved as replacements for the M73B1 (in this video, we will take a look at one equipped with an M84, the optic adopted for the later M1D).
The US Marine Corps, of course, had to be a bit different, and adopted their own sniper rifle variant in 1941, a 1903A1 fitted with an 8 power Unertl scope. These scopes were a tradeoff, being significantly more fragile than the M73B1, but also being much better for long range precision shooting. The USMC, taking much pride in their culture of marksmanship, was happy to make that trade, and the rifles served well throughout the war.