I don't know, and I bet ants don't, but you'd have thought that someone would. I am about to conduct an enquiry in real time, and my starting point is a page on biomass on Wikipedia which says (currently) that there between 10 to the power 7 and 10 to the power 8 billion ants, weighing between 900 and 9000 million tons. This seems a very broad church, even for something as hard to count as ants.
OK. On Google Answers, a Harvard ant expert called EO Wilson says there are between 10 to the power 16 and 10 to the power 17. Is that the same as the above? Yup, if you do american billions with nine noughts. So we have a generally quoted answer, but that zero makes a real difference.
The source given in both cases is the 1983 book, Collection of Amazing Animal Facts by Joan Embury with Ed Lucaire. Pardon me if I am not reassured, since this book actually says there are a 'quadrillion ants' which is the lower of these two numbers. Which is fine, but the bigger of the two numbers gives us 8100 million more tons of ants to worry about.
Quite a lot of other websites say that ants weight something like the same as humans, but human biomass is a pathetic 100 million tons. Basically, when you are looking for answers you would be happy to quote to an alien invader who says he will kill you if you get the answer wrong, the internet is sometimes not (yet) very reassuring, because the same not very brilliantly substantiated facts turn up in all the obvious places. I am sure I could find something better if I didn't have to go and make supper. It's the story of my life.
(Which is why my fiction is unautobiographical.)