This question is impossible to answer since there are no other references to climate, location, type of cows, condition of pastures, how they're raised, how they're pastured, soil, type of vegetation, and topography that could otherwise directly determine the closest estimation to stocking rate that you are asking! Stocking rate is determined by the number of animal units per month that can be grazed on a pasture, no matter the size. As for the raising part, that all depends on the size of the cattle, since that has an effect on the space requirements per animal.
Since you are asking "how many cows can you raise or pasture per acre? " I'll ask you these in return: Are you raising them in a dry-lot like a feedlot, or pasture or both? Where do you live (particularly for pasturing cattle)?
United States? Canada? Australia?
And where in USA, Canada or Australia or some other nation you come from? I don't mean what state or province, oh no, I mean where in that state or province, because the factors affecting stocking rate differ greatly between areas within a state or province than between states or provinces What climate do you live in? Mild?
Defined seasons? Hot and humid? Cold in the winter and hot in the summer?
What type of cows are you referring to? Dairy? Beef?
Smaller or mini breeds like Dexters or Mini-Angus? Or large breeds like Charolais, Simmental, Chianina or Limousin? Or are they medium-sized cattle like Hereford and Angus?
What sort of cattle are you referring to? Bulls? Cows?
Steers? Heifers? Calves?
A mix of some or all of the above? What is the average weight of these animals? Cows : What type of cows?
Dairy or beef? Bred or Open? Young or old?
Lactating/suckling a calf or dry? What gestation period are they in? Bulls: Are they growing or mature?
Young or old? Coming off of breeding cows or not? Steers: Are they being backgrounded/stockered or finished?
Heifers: Are they being fed as replacements or as stockers? Calves: Are they on their mothers, raised as veal calves, just weaned or bottle babies? If they're on their mothers, often the stocking rate is determined by the weight of the cow and calf together as one unit.
But not if they're raised as weanlings , veal calves or bottle calves What condition are your pastures in? Excellent? Poor?
Are the grasses just starting to pop up, or is there grasses that are seeding out? What kind of soil do you have? Sandy?
Loamy? Clayey? A little of everything in between or one or more of either or?
Have you had a soil test done on your pastures to see what nutrients are missing? What are the main type of grasses you have growing in your pastures? What native vegetation grows well where you are, in terms of trees, shrubs, forbs/legumes and grasses?
And finally, what kind of topography do you have? Is it flat with rich fertile like the prairie or on the Corn Belt, or hilly and rocky like in the Appalachians or Foothills near the mountains? Most of the above questions should be answered before you find out how many cattle you can graze per acre.
Some areas have enough forage and have a mild climate that allows a stocking rate of 2 cows/acre/month. Other areas where it is more drier and desert-like a person can only stock 0.25 cows/acre/month. Since we have no other way of knowing what other conditions you live in, we can only assume.
And 99% of the time our assumptions may very well be wrong Check out the following related questions that has been answered on this similar subject matter for more info.
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