You either have ground movement cracking the concrete, or the handrail anchors weren't properly surrounded with decking.
Do you have a decorative overlay on the deck, or is it bare concrete? Either way a patch will show, some worse than others.
If the handrail seems stable and you just want to keep water/ice from creating further damage, you're best (read easiest) bet is a rubberized seam sealant. Home Depot carries SikaFlex, I believe they have grey and tan. It's the consistency of syrup, therefore self-leveling, so be careful with it. If the crack is deep you'll want to fill it with sand to within an inch of the top. That should keep for a while, even with usual ground movement and concrete expansion/contraction.
If the rail is wobbly, I'd say you have an insufficient base and need to dig out the anchors. Replace them with new and put some good concrete around them. When I core drill into a deck for new rails, or dig out and replace old anchors, I fill the area around the anchors with hydraulic cement. It dries fast (good for keeping the anchors true) and hard. If you have to replace the anchors let me know and I'll fill you in on making a jig to keep the anchors spaced correctly and level.
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