No. This rifle should be 7.65 Argentine.
I know that www.ammunitionstore.com has some very nice surplus right now.
Your rifle shoots 7.62 argentine. I think remington may have a factory load for it. The 7x57 mauser brass is a little longer and would not chamber in your rifle DO NOT TRY.
Argentina was weird in that they wanted this caliber while the rest of South America wanted the 7mm mauser. Both rounds came into use about the same time.
I have a chilean mauser from the same period but in 7mm shoots great. If the barrel is good you should have a shooter.
Go to a smith and have the barrel slugged to verify the caliber. just to be safe.