What kind of elbow? Double hinge or the swivel hinge kind?
If it's one of the rods from a double hinge, just use a plastic rod that's the proper size and slide it in there, then mushroom the ends with a mallet.
If it's the swivel-hinge kind where a peg pops into the upper arm, you'll probably have to use a screw to replace the snapped peg.
I'd say complete replacement of the joint/arm is the only way to retain the articulation. I don't move mine around much so I would be lazy and glue it back together, foregoing any possibility of changing the pose down the road.
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If it's one of the rods from a double hinge, just use a plastic rod that's the proper size and slide it in there, then mushroom the ends with a mallet.
If it's the swivel-hinge kind where a peg pops into the upper arm, you'll probably have to use a screw to replace the snapped peg.