Can you put new rings in your engine without changing bore size?

Unfortunately this is not a simple "yes/no" question.

Sometimes an engine can be disassembled and there is little if any cylinder wear, especially if the oil has been changed regularly and the engine has been properly cared for. If there is no wear you can hone the cylinder walls and put new rings in, provided that the pistons are also not worn. Obviously worn pistons need to be replaced as well.

If the cylinders have as little as a couple thousands of "taper" you need to have the cylinders bored and replace the pistons/rings with an over-sized version. That kind of cylinder "boring" doesn't change the displacement enough to make any significant difference.