Well, that's going to depend. The water that is coming out of your sprinkler is coming out a small hole in the sprinkler. Drops of water in the air are roughly spherical due to the surface tension of water, so the water droplet will be a sphere with a diameter equal to the diameter of the whole.

The volume of a sphere is:
(4/3) * pi * r³
where r is the radius (not diameter) of the sphere.

Could you collect a number of drops in a little weighed container and then weigh it with the drops of water in it?That's what I did once when I wanted to figure out how thick a layer of water I had, sandwiched between 2 layers of mica. From the density of water, you can figure out how big a volume of water you'll need to collect to be able to weigh it on the most sensitive scale you have.