It APPEARS to be a cannonball. But let's see if it matches an actual cannonball's specifications.
First... does it have any kind of hole in it, approximately an inch to 1&1/4-inch in diameter? (For holding a fuze.) You didn't mention one, so I'm assuming it is a solid (not hollow) ball.
Then:
(1) Actual cannonballs are always as "truly-round" as a glass marble - no lumps, bumps, or significant flat areas. An irregular shape could cause the ball to jam in the barrel upon firing - perhaps cauusing the cannon to burst. So the balls were inspected for imperfections before they shipped out from the Foundry, and again at the Arsenal.
(2) Actual cannonballs were very carefully manufactured to be a very specific diameter and weight ...because they had to fit the cannon's bore precisely (not too tight nor too loosely). So we'll need you to do very precise measuring of your (presumably solid) cannonball, and compare it with the listings of actual cannonball sizes at
http://www.civilwarartillery.com/shottables.htm
By the way, the size-&-weight Specifications listed in the US 1861 Ordnance Manual are the same for Confederate, pre-civil-war US, and Colonial-era European solid-shot cannonballs.
The nearest caliber for the size you mentioned is a 5.82-inch caliber cannon (called a "24-pounder"), whose projectiles were 5.68" in diameter. The solid-shot for that caliber of cannon weighed 24.3 pounds. Please weigh your cannonball on a precision scale (most household bathroom scales are off by a couple of pounds) and let us know the churchyard-ball's precise weight. That, along with its exact diameter, will tell you whether it is truly a cannonball or not.
Regards,
TheCannonballGuy (PCGeorge)