In practice, they tend to be used interchangeably. But if you don't intend to say that you tore the paper rather savagely, I would suggest using "tear".
"Rip" suggests that the paper was torn in a fierce and savage manner, probably destroying part of the material in the process.
Bear in mind that the english language is full of collocations. There are some words that are commonly used together. 'Tear', for instance, is often used with "cloth", whereas 'rip' with paper. But that does not mean you will not come across different usages.