If the rod is small enough to fit down a .22, buy a .22 patch jag that fits the threads on your rod.
If not, just get a .22 cleaning kit.
I personally prefer the brass pistol cleaning rods from Brownells, a .22 rod for rifles, and a larger shotgun rod. That way, I just grab the rod I need off the rack, rather than getting out a kit and putting what I need together.
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