No you CANNOT use 7.62x54 ammo in your .308 rifle.
You should however be able to use 7.62x51
From another forum...plus this has been discussed here previously IIRC
OK --- Let's address the oft-posed question "Are the .308 Winchester and 7.62x51 NATO one and the same?"
The simple answer is no. There are differences in chamber specs and maximum pressures.
The SAMMI/CIP maximum pressure for the .308 Win cartridge is 62,000 psi, while the 7.62x51 max is 50,000 psi.
Also, the headspace is slightly different. The .308 Win "Go Gauge" is 1.630" vs. 1.635" for the 7.62x51.
The .308's "No-Go" dimension is 1.634" vs. 1.6405" for a 7.62x51 "No Go" gauge. That said, it is normally fine to shoot quality 7.62x51 NATO ammo in a gun chambered for the .308 Winchester (though not all NATO ammo is identical).
Clint McKee of Fulton Armory notes: "[N]obody makes 7.62mm (NATO) ammo that isn't to the .308 'headspace' dimension spec. So 7.62mm ammo fits nicely into .308 chambers, as a rule."
You CAN encounter problems going the other way, however. A commercial .308 Win round can exceed the max rated pressure for the 7.62x51.
So, you should avoid putting full-power .308 Win rounds into military surplus rifles that have been designed for 50,000 psi max.
Reloaders should also note that military ammo often is made with a thicker web. Consequently the case capacity of 7.62x51 brass is usually less than that of commercial .308 brass.