Both are correct and natural. I would say "I often have my teeth cleaned in order to remove the plaque (or to have the plaque removed)." I don't like the word "get". It's perfectly good English, and it is fine in many common expressions. The problem is that the word simultaneously means everything and nothing. There is usually a better word to use.

I often clean my teeth to remove plaque. I often get my teeth cleaned to remove plaque. Both are correct but second one sounds more accurate.