Much depends upon the specific animal in question, the fertility of the land, the weather, and the regional climate, and other parameters.
Lower Bounds
However, in the US Midwest, using modern agricultural techniques, in a typical year, and using high intensity farming, hobby farm enthusiasts estimate that it takes 1 acre of farm to support each person for a year. However, in the US Midwest, using modern agricultural techniques, in a typical year, and using high intensity farming, hobby farm enthusiasts estimate that it takes 1 acreCarrying capacity ($C_{Human}=\frac{kg}{km^2}$)
Estimated human population ($P_{human}= 1$)
Average Individual human mass ($M_{human}=100 kg$)
Area of farm to support each personCultivation (estimate at 100 kg$A_{\text{Farm}} = 1 Acre = 0.004 km^2$) for a year.
I realize this doesn't actually answer your question but it should give you an idea on the lower bounds of acreage required to support a creature.$$C_{Human} = \frac{P_{Human} \times M_{Human}}{A_{\text{Farm}}} \rightarrow \frac{1 \times 100 kg}{0.004 km^2}=24,710 \frac{kg}{km^2}$$
Real Life Example
A real life estimate for natural carrying capacity could be derived from the bison population of the American plains prior to major European settlements.Probably a better method would be to estimateMultiply by the bison population of the American plains prior to major European settlements, multiplybison by thetheir average weight for the bison, and then divide by the area of that region.
Carrying capacity ($C_{Bison}=\frac{kg}{km^2}$)
Estimated Bison peak population ($P_{bison}= 60,000,000$)
Average Individual Bison mass ($M_{bison}=700 kg$)
Area of Great Plains ($A_{\text{Great Plains}} =1,300,000 km^2$)
$$C_{Animal} = \frac{P_{bison} \times M_{bison}}{A_{\text{Great Plains}}} \rightarrow \frac{60,000,000 \times 700 kg}{1,300,000 km^2}=32,307 \frac{kg}{km^2}$$