It depends on the material - if it's plastic, I definitely wouldn't burn it! - and certainly not in the fireplace where I roast food. If it's cotton (it can be burned just fine) or wool (yeah - that would stink - you'd have to make a big fire and put the rug in small pieces), you can burn. But - don't you have a municipal waste collection point nearby? - it would be easiest to take the carpet there ...