I have planted a lot of food plots over the past 25 years, and let me recommend something to you that is easy as pie. You don't have to plant it now. You can wait till the end of summer.
Clear it out the ground real well. Spray it now with Roundup herbicide, which kills absolutely everything it touches. Use at least 1.5 times the recommended strength. For a plot as small as 20 x 40, you could even use a hand sprayer to put the herbicide down. (Use a 5 gallon hand tank size).
Everything will be dead in about 4 weeks.
Then, about the 3rd week in August, till it up. You can use a walk behind garden tiller to do this. Then throw down/spread by hand some lawn fertilizer. Any "starting" type lawn fertilizer will do. Let this stay down for about 10 to 12 days, and hopefully soak in with rain.
Then, just hand spread Annual Rye Grass. Put it down really thick.
About two weeks later, the Annual Rye will come up, really thick. Within 3 weeks, it should be knee high.
When the fall comes, deer love to eat this brand new green rye grass. While everything else green is dying, this nice tender tall grass is sprouting. It will continue to grow very well into the winter, even after you get your first or second really hard freeze. It is there, and growing in the cool weather, and the deer will be really really attracted to it.
I have planted soybeans, and I don't recommend it. They will come up in early September, but before they even get two inches tall, the deer will pluck them out of the ground, which totally kills the plant. Crows and other birds will also pluck them out, to get what is left of the bean at the bottom of the sprout. You will see a fair amount of activity for 10 days or so, but then all of the sprouts are plucked out, or snipped off, and you will never be able to get the beans to grow thick. Also, soy beans will not grow well unless your really till the soil up fine. They require fine tilled soil, plus having the soil compacted down on the bean. (Otherwise, the beans in the ground will simply rot, not grow.)
Annual rye, however, does not require finely tilled soil, or compaction. No matter now much the deer eat it down, it will still keep growing back, and very fast. Also, you will attract turkeys to it, who want to walk through it to find grasshoppers and crickets. (It becomes their "bugging" ground.)
For the quickest and easiest deer plot, try the annual rye grass.
You can use wheat seed instead, but it is hard to get wheat to grow thick (without dying) and it is much more expensive than rye grass.
If you want to create activity right away, mix a small bag of soybeans into your rye grass and spread it at the same time.
Best Regards,
Big Paulie