In written english it is not correct and only written in very informal writing that mimics speaking. In speaking, there is a range of pronunciation between 'want to' and 'wanta' and 'wanna'. One direction is more correct, the other is infomal verging on childish or baby talk. If you think of it as 'baby talk' you can understand that it might be used between friends (or lovers). Also, as you speak english more quickly, these abbreviated pronounciations become more common. In fact, people use them this way all the time. I can't say I'd tell a language speaker that they're 'correct', but you should understand them and I think you should know how to use these words.

Here is an explanation: http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv165.shtml Wanna and gonna are frequently used in speech in informal colloquial English, particularly American English, instead of want to and going to. You will also see them used in writing in quotes of direct speech to show the conversational pronunciation of want to and going to.

Wanna and gonna are examples of American slang. English learners should avoid using slang when they are writing or speaking. This is because most of them don't understand the meaning and usage. 1. Wanna = want to. I want to improve my English. 2. Gonna = going to. I'm going to study hard.