Sweaty hands is a common ailment for weight lifters and rock climbers, with equally detrimental effects.  The solution really isn't nutrition related.  It's simply **chalk**.  Chalk dries the hands, and improves your grip.

If you feel that chalk would be detrimental to the environment, you can go for an ["Eco Ball" by Metolius][1].  Same effects, although I might argue that it is not quite as effective as good old fashioned chalk.

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After reading the comments, you also may want to look at this article on [diet and hyperhidrosis][2].  The thing is, you do need to rule out whether you have hyperhidrosis or not.  Take a look on at [this article that describes what hyperhidrosis actually is][3].  It also has tips on food to avoid in addition to other tips.

Also do remember that rock climbing is an activity that causes an adrenaline rush, and is therefore stressful.  Not necessarily in a bad way, but it is a factor to consider in trying to understand the sweaty hands.


  [1]: http://www.metoliusclimbing.com/eco_ball.html
  [2]: http://www.prlog.org/10224407-hyperhidrosis-diet-tips-to-stop-excessive-sweating.html
  [3]: http://www.disabled-world.com/health/dermatology/skin/hyperhidrosis.php