Interesting question! For most ant species (there are over 12,500 ant species) we do not know how many chromosomes they have. This is true for most living organisms.
For the ~750 ant species that have had their chromosomes counted the number varies greatly. For perspective, humans have 23 pairs of chromosomes, while ants can have 1 to 60 pairs of chromosomes. In fact the ant Myrmecia croslandi has the least number of any known organism with only a single pair of chromosomes (one pair in the females since they are diploid, while the males have only a single chromosome since they are haploid).
If you want to read more, Lorite & Palomeque (2010) recently wrote a review article on this topic that you can find here.