At that size, the effect of surface tension becomes so strong that you can almost treat the drop of water as a bag of water. According to this video from V Sauce, if you were the size of an ant, water would be 21,000 times thicker than it seems to us at normal size. The same phenomenon allows ants to walk on water:
Or carry droplets of water (thanks to Hypnosifl for this picture):
And allows some spiders to wear incredibly stylish water droplet hats:
In addition to the effects of surface tension, it appears that the outer shell of an ant, called a "cuticle", is naturally hydrophobic (i.e., water-repellent), which would make it even easier for an ant to "hold" a droplet of water. If you find a "raft" of ants (which occur when a colony is flooded), you can push it down as hard as you like, but it will keep bobbing back up to the surface, because their hydrophobic shells just refuse to stay down:
The combined effects of surface tension and hydrophobic cuticles allow ants to survive underwater for as long as 2 weeks by breathing air trapped in tiny bubbles around their bodies:
The incredible strength of the surface tension of water isn't as familiar to us as it might be to tiny creatures, but the same dynamic is at work when small objects with little or no water displacement float, or when you overfill a glass of water and this happens: