Yes, your .308 Winchester can be rechambered to .300 short magnum, BUT:
1. bolt face and extractor will have to be opened up to accept the larger rim.
2. receiver rails will have to be opened up to give reliable feeding. Feed ramp may have to be reshaped too.
These are standard gunsmithing operations, but no guarantee that the rifle will shoot as well or be as reliable as it is now in the original caliber.
Why not just sell/trade your rifle and get the caliber you want?