Is there a device that I can plug my refrigerator into, that will cycle the fridge on and off in order to save energy?

Your refrigerator already has a thermostat that does just that. If you cycled it off more than the thermostat calls for, its internal temperature would rise, introducing food safety and spoilage risks.

The cheapest and simplest device I know is one of those electrical timers you can get at the hardware store. You will have to get one with multiple on and off pins if it is not digital, then you just plug it into an electrical socket and the fridge into it if you want a device that takes the fridge out of the picture.

Similar to this http://www.amazon.com/dp/B001IQ3RWS/ref=asc_df_B001IQ3RWS1572098?smid=A3GWNQKI7JPDAL&tag=pgmp-901-95-20&linkCode=asn&creative=395129&creativeASIN=B001IQ3RWS

As long as the door remains closed “cold loss” (actually “heat infiltration”) is purely a function of the refrigerator’s insulation capability and the difference in temperature of the room.
There are some tricks you can play to reduce refrigerator operating costs.

Before you do this, get a Kill-a-Watt unit so you can see how much you saved.
1) Move it away from the wall an extra inch so you have better air transfer to the coils.
2) Vacuum and clean the back side.
3) Make sure the fan and area underneath is clean.
4) Keep it full so you lose less cold air when you open it. Use water bottles or cold packs if you have them. they wil also keep it cold longer if you have a power failure.
5) Cover the ice maker hole with insulation on the inside and don’t use it. They are notorious for leaking.

If you have air conditioning, every watt you save by making your fridge run better actually counts a little more than double since your A/C does not have to get rid of the heat.

Don’t invite me over to have dinner. You are going to have food spoilage.
@worriedguy hit the nail on the head, all five points. The other thing is if the refrigerator is over eighteen years replace it with an “energy star” and you MAY get a tax credit.

If all you’re using the fridge for is to keep beer or some other nonperishable item cool at specific times, then there’s no problem with hooking it up to a common timer or timed breaker. But if you use the thing at all for food that must be kept frozen or normally cool (40°F is common for cooked foods), then I wouldn’t try to out-think the designers of the appliance. If it’s working properly it already does exactly what you want.

A thermostat.

Yep. Interestingly enough most refrigerators already have one build in. It’s called a thermostat. There is generally a knob inside the box that lets you adjust the temperature. When the falls below the set level the compressor cycles off to save energy and when it rises above the set temperature it turns on to cool things down.

I don’t get it. Why would you need a separate device? As worried guy said above, oneof the best and simplist ways to save some energy is to keep it very full. It is not so much air escaping it is that cold liquid or frozen food and ice is colder than air so to speak…sort of. Think about it, you could stand outside in 30 degrees for a while, it would be cold, but you would not become hypothermic immediately. Spend a few minutes in 50 degree water and you begin dying very fast from the cold. Holding ice in a bear hand becomes painful fast.

Dunk a hot coke can in ice water, cold in minutes. Stick it in the freezer wait a lot longer.