Why does caffeine powder cause apple cider (or any carbonated drink?) to foam?
I don't need to know why you're mixing uppers (caffeine) with downers (alcohol) but if the powdered caffeine is removing the fizz from your cider then you might try dissolving it in hot water first and then adding the hot caffeine solution to your cider.  In dissolved form, the caffeine cannot provide the nucleation sites for the formation of CO2 bubbles that MaxW and vapid pointed out.

The solubility of caffeine in water is 200mg/ml at 80 oC so you should be able to dissolve an adequate dose of caffeine in a small enough quantity of hot water to avoid both excessive warming of your cider and precipitation of the caffeine upon cooling and dilution.

It behooves me to mention that recommended caffeine administration should not exceed 200mg every 3-4 hours in adults, but since you're adding it to alcoholic beverages, I doubt you give a monkey's.  Here's the drugs.com link anyway:

https://www.drugs.com/monograph/caffeine-caffeine-and-sodium-benzoate-injection-caffeine-citrate.html

And solubility data here:

http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Sigma-Aldrich/Product_Information_Sheet/c0750pis.pdf