These guys seem to offer some products in that space however it seems many of them are of the remote control variant (not fully automated). Crop dusting is a pretty routine task and you could easily program a drone to cover a specific field at a given time and let it do its thing. The main issue you will face in the current market is simply useful load. Ignoring the military drones out there most of the commercially available unmanned vehicles are on the smaller side and simply don't have the useful load of something like a Piper Pawnee that is used for current crop dusting.
It does seem that the FAA has approved some drones for this use but that was recently so Im sure it will be a little while before we see them. Although it seems Japan has been using them for this purpose for some time.
So yes tank carrying drones do exist (but I cant find the volume of the tanks, they do however appear pretty small).
FWIW any small drone could be modified to carry a tank and spraying device provided it could lift it. All things considered people have built some pretty big RC planes