Looks like a decent old sporterizing job, did your Grandpa do it himself? If so that's quite a keeper - a family heirloom kind of thing.
Are you sure it's the barrel turning? You can tell by looking through the sight or just eyeballing the front sight. The blade should be straight up vertical when the receiver is also vertical.
You can wiggle a loose barrel back and forth a little, or maybe even screw it right off with that sling screw missing. But it's not the screw that holds the barrel tight.
As described above the barrel is torqued on, "crush fit" in a way. A new one never installed will still be some 20 degrees off vertical when snugged on and has to be tightened on with a special wrench with a long handle on the receiver while the barrel is held in a type of vise that won't mess it up while holding it tight. These are special tools just for the one purpose and if you don't have them then you probably can't do it yourself. If you try you'll likely mess up the finish on the rifle, at least.
Barrels on those sometimes shoot loose especially if they've been removed and installed a few times. What happens each time it's torqued on is that the machined shoulder that fits against the receiver gets squished (or crushed) down a very little bit. It only takes a few .001" thousandths of an inch to lose that 20 degrees of squishing that holds the barrel on tight. Threadlocking products shouldn't be needed or used.
The shoulder can be pushed back up by someone with a lathe if they make a bit of tooling that looks like a knurler but uses a hard bearing instead of a cutting wheel. That tool can be driven against the shoulder to move the steel just a little, enough to restore the barrel's squish.
I'll stop here but this is not the end of the project. If it sounds complicated or you think you might not be equipped to do these things give your rifle to the local gunsmith. He'll know what to do. You've got some very fine gunsmithers in your state.
