Check out some appropriately sized ladder or step rungs. Larch is light and naturally rot resistant.
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Good place to start - for indicative measurements.
However, bear in mind that, unlike Jacobs ladders, the rungs on ratlines are exposed to the weather 24/7 and so they need to be quite substantial. Their state has to be closely monitored on a regular basis. Even if they are put there merely for a more 'nautical' look, chances are that sooner or later they will be used in anger.