Yes, although technically it's 7.62x51 instead of .308
From Wikipedia:
Although originating from an identical preceding series of experimental cartridges, the commercial 1952
.308 Winchester and the military 1954 7.62×51mm NATO chamberings have evolved separately but remain similar enough that they can be loaded into rifles chambered for the other round, but the .308 Winchester cartridges are typically loaded to higher pressures than 7.62×51mm NATO service cartridges.
[26] Even though the
Sporting Arms and Ammunition Manufacturers' Institute (SAAMI) does not consider it unsafe to fire the commercial .308 Winchester rounds in weapons chambered for the military 7.62×51mm NATO round, there is significant discussion about compatible chambers and muzzle pressures between the two cartridges based on powder loads, chamber dimensions and wall thicknesses in the web area of the military compared to commercial cartridge cases.
[27][28] As the chambers may differ accordingly the
head space gauges used for the two chamberings differ.
[29]