Ah, I see. Civil War technology permits the use of vast quantities of gunpowder; look up the Battle of the Crater. Reading through this thread again, I would have to disagree with @Naomasa298 that this giant would necessarily be able to kick over castle walls. That would really hurt, and human feet aren't made for it. I screwed up my big toe for months just from kicking a soccer ball the wrong way. If he had a sledgehammer he could do it for sure.
Keep in mind castle walls were not big lumps of concrete, they are huge blocks wedged together. But if you're that big those massive blocks become very small. And knocking over a small stack of rocks is pretty easy.
I disagree with the idea that cannons wouldn't hurt him. It is unfair to only consider heavy field artillery designed to counter infantry columns (12lbers) when it comes to facing a giant. There, any sane nation would wield naval or siege guns. Let's take a Krupp naval gun for reference from the Civil War era. Projectile was 150kg and the muzzle velocity 580mps. Translate to a momentum of 87000 kgmps declining over a distance of five kilometres. That's the same force as an average car sliding into you at 160kmph (100 mph). Those cars wreck buildings and vegetation when they slide off the motorway. There's a chance it would disbalance a giant, not the least hurt him.
I suppose. But a giant can stub his toe just as easily as the rest of us. I see no reason why a sledgehammer wouldn't be preferred.