Rasta comes from the root word Rastafarian...I'm not going to give you the entire Rastafarian Movement run down; if you don't know look it up. Pasta Rasta's know little, if anything, about the Rastafarian movement & culture and are usually just dirty hippies or street rats.
Pasty Rastafarian doesn't have a real nice ring to it so that is where you get the term Pasta Rasta.
The term originated sometime in the early 90's in the bay area where several Pasta Rasta's live and (some times) work (sometimes not so much, with the working and the whole "being a productive member of society" thing)
Since, for white people, the formation of true dreadlocks generally requires a sustained lack of personal grooming, the Pasta Rasta are at an attractiveness disadvantage from the get-go.