The reason why tigers don’t live in Africa is because they evolved in Asia and there was a physical barrier of water (see map) between Asia and Africa which prevented the migration of the tiger to Africa. Could the tiger live in Africa today? Large parts of Africa has the wrong habitat (too open and dry) but equatorial Africa is heavily forested so I’d day the tiger could survive in parts of Africa today. There is no point relocating it there though because they are chopping down all the forests!
Some say the tiger originates from Siberia and during evolution it migrated south to Indonesia and west as far as the Caspian Sea. It was also present in Alaska which means that there must have been a land mass or land bridge then joining Russia and America where there is now sea (the Bering Strait).
The earliest record of a relative of the tiger we are told comes from Northeast China 3.2 m years ago. The earliest fossil record is dated 1.5 million years old (this is written 1.5 Ma).
The water barrier theory that I present here is more or less mine because my research failed to throw up a good answer. If you have a better one please leave a comment and tell me. My answer is based on the reason why there are no wild cats in Australia other than feral cats which are domestic cats imported on ships turned wild.
The reason is the same; there was a physical barrier, a water mass, preventing the migration of the early wild cats of Asia to the Australian continent. The picture shows the Wallace Line. Link to the page.