How could I perform a power analysis of a permutation (randomized) test?
Also if you know some R package I would be greateful for any recommendation.
You can do this using simulation.
You first need to decide what you want your data to look like (which distribution(s) and parameters) and how you plan to analyze it (what statistic are you comparing in the permutations?).
Then write some code that will generate your data and analyze it. Run the code a bunch of times and see how often you see a significant difference, that gives you the power.