I think I have the same problem.
I use Vantage theme at wordpress.org. I’ve uploaded republika font, I’ve selected headlines and it works for headlines.
Then I followed these instructions for the top menu but it didn’t work for me. I’ve also tried #site-navigation li a but stil no results.
Is there any other thing I could try?
Thanks Dinesh, my site is offline for the moment but I found a solution in the meantime.
I installed the plugin “CSS Site Origin”, it allowed me to change the font of my menu, I just had to tipe “republika” in a case.