I'd like to say something from the farmers' perspective--get a fence. Your chickens have no right in his field. Although the crop losses to your birds are probably small, they are still crop losses. People seem to think that because a farmer has acres and acres, it's OK that they lose a little. But in reality, it's no different than if you allowed your chickens into your neighbor's garden. The farmer prepared the soil, purchased the seed, planted, and cared for those plants. He has enough loss from wild birds without you adding your birds to it, and asking him to alter his behavior to boot.
Put up the fence, and let him know your concerns about overspray. He'll be a lot more likely to listen to you when your concern isn't "I'm worried about what my chickens will get into while they trespass on your land and eat your crops."