Can you jailbreak an iphone 4s ios 6.1.3?

Please, I would like to know if you can do this.

No!
There are some sites like evad3rs.net, which keep saying that their jailbreak is ready for use and even provide some download links, but don't believe them - It's just silly fake, oriented specially on trustful users and making them to complete payed surveys in order to get "fake" download links.

Jailbreak for 4s on 6.1.3 isn't out yet, be patient.