Well yes!
Man has been conducting different experiments over the years to artificially inseminate animals especially the species that are fast approaching extinction.
Man also injects the animals with high level hormone drugs to induce a sort of "horniness"in the animals that will encourage mating and a better chance of Pregnancy in the animals.
Another method is putting few males in a pen or cage with more females so the males can have unlimited and indiscriminate access to females to mate with to get them pregnant and produce offspring.
But if you mean can a human being actually impregnate an animal?
That's disgusting. No.
This is because for fertilization to even take place, both organisms mating must be related down to the same specie. This is why even though the chimpanzee is our closest relative, you cannot impregnate a chimpanzee. Not that you would try, right?