How is Lord Acton's famous quote, "Power tends to corrupt, and absolute power corrupts absolutely,” applicable to George Orwell's Animal Farm?

Lord Acton's belief about the corrupting nature of power can be seen in the political landscape that defines Animal Farm.
One of the reasons why Orwell's novel is so powerful is because it is a study of political power. Whoever is in political control of the farm displays corruption. As the novel opens, Farmer Jones is corrupt. He abuses and exploits the animals because he can. No one is able to challenge his authority. Part of the reason why Old Major's appeal resonates with the animals is because he is right in expressing Farmer Jones's corruption: 

And you hens, how many eggs have you laid in this last year, and how many of those eggs ever hatched into chickens? The rest have all gone to market to bring in money for Jones and his men. And you, Clover, where are those four foals you bore, who should have been the support and pleasure of your old age? Each was sold at a year old—you will never see one of them again.

Jones is corrupt because he has unfettered political power over the farm. He is able to do whatever he likes. He does not display any regard for the animals' feelings. He embodies what Old Major calls "the tyranny of human beings" because he exercises political power without any limitations or checks on his autonomy.
Motivated by Old Major's theory of "Animalism," the animals wage a revolution to overthrow Jones and the humans. After its success, Manor Farm is renamed "Animal Farm." The pigs assume power in the name of all the animals. Over time, though, the pigs, specifically Napoleon and Squealer, begin to display the same trappings of power that Jones displayed. They learn to read and begin to consolidate political control of the farm to maximize their benefits. Squealer uses propaganda and media manipulation to ensure complete deference to "Comrade Napoleon." For his part, Napoleon uses the dogs as his private army. Once he is able to develop political security through force, he exiles Snowball and represses all dissent. Power and control motivate Napoleon. Like Jones, he abuses the animals and bullies them into submission. Like Jones, he takes advantage of the animals' labors because of the strength of his political position. Under Napoleon's leadership, Animal Farm becomes "the tyranny of the pigs."
Both displays of political control show how "power corrupts" and that "absolute power corrupts absolutely." Jones and Napoleon do not exercise power in a shared and collaborative manner. Their display of power is absolute and unchecked. As a result, they embrace corruption because they can. They are able to act outside of the law because they are the sole arbiters of power in their political communities. At the end of the novel, the farm has been renamed again and the animals are unable to differentiate between pigs and humans. This underscores how corruption is a part of the human and pig autocratic displays of power in Animal Farm.