Yes, Albert Einstein did have pets.
Einstein was known to be an animal lover. While his cat Tiger seems to be the most well-known, he also owned a dog and a parrot. The reference quote states, “If a man aspired towards a righteous life, his first act of abstinence is from injury to animals,” he said, and was himself known to own multiple pets, including a dog and a parrot. But it was his cat Tiger who seemed to get the most attention, at least as far as posterity is concerned.” This suggests that Einstein held animals in high regard and acted upon that belief by keeping them as companions.