Hi Navitasan
Both choices are grammatically correct. But this is not only with "any", but also with:
either of, neither of and none of. For instance:
1) Is (or: Are) any of these children mischievous?
2) I wonder if either of those alternatives is (or: are) practical.
3) Neither of these cameras works (or: work) properly.
4) None of the plants has (or: have) grown very much.
Hope this helps.
Cheers!