Can you shoot 45 acp ammo in a Glock 37?

Nope. Matter of fact, you can't even load it. The .45 Automatic Colt Pistol (ACP) cartridge is longer than the .45 Glock Automatic Pistol cartridge (GAP). And the model 37 IS in .45 GAP. Both rounds headspace off the case MOUTH- the .45 ACP is too long for the slide to go into battery (close the action). And, with the exception of some revolvers, you cannot shoot .45 GAP in an .45 ACP firearm.