It really depends on a lot of things... Are you doing it yourself, or are you going to hire it done? What do you want it made out of? Chain link, cedar boards, vinyl, wrought iron? It all makes a huge difference.
I had a wrought iron fence put in for $50 per foot a few years ago, and now it would cost $75 per foot for the same thing. I put in a 6 foot cedar board fence at a rental house for only about $5 per foot, but the bids that I got from fencing contractors ran from $14-$42 per foot. And, if you're only going to string barbed wire, then it'll be even cheaper.
Just remember, your going to need around 832 feet of fencing to get around your acre (208 feet per side), so every $5 per foot is going to cost you an additional $4160.
What you need to do is just have your local fencing contractors come out and give you some bids. They will give you the bids for free, and it's good to know how much the professionals are charging, before you go to Home Depot and check out how much it would cost you to do it yourself.
Here are some companies that set up contractor bids for homeowners for free, from contractors that they've worked with and/or checked out. They'll usually set up between 2 and 4 bids for you, based on your time schedule, so you don't have to deal with it. Otherwise, you're going to want to check with your local BBB, or websites like Angie's List, which will give you reviews of local contractors before you call them. (Angie's List charges a fee to access.)
eLocal USA: 888-302-2093
iHome Experts: 877-386-4108
Service Magic: 877-640-0905