It is possible to rent a server and mining his bitcoin?
Yes
If you mean that you are looking for some hashes to buy.
You can buy some hashes from companies. You can buy a mining contract.
You can check a link in my signature - this is example of mining contract services.
There are plenty of other similar services like that one from my signature, but before you buy anything remember to read around about it.
Here you have a thread from Lunamine
https://bitcointalk.org/index.php?topic=675315search around this section for more of similar services. :
https://bitcointalk.org/index.php?board=84.0also read :
https://bitcointalk.org/index.php?topic=317001.0 <- very interesting if you are thinking about Cloud Mining
