What is the time complexity of java.util.Collections.sort() method?

You should have found it in the API: n log(n).

You could have read up the docs on Collections sort, but here it is for you:

The sorting algorithm is a modified mergesort (in which the merge is omitted if the highest element in the low sublist is less than the lowest element in the high sublist). This algorithm offers guaranteed n log(n) performance.

Your Comparator doesn't change this complexity, unless you do anything with loops over your collection in it, which you don't.