Why not add a cleaner to your oil like Marvel Mystery Oil, AutoRx, Kreen, or Archoil?
Of course everyone will suggest Mobil 1 HM or Valvoline MaxLife HM, but these clean fairly slowly IMO.
An ester-based oil (like Redline, Silkolene Pro, or Motul 300V) will do a very thorough cleaning in 1 - 2 oil change intervals, but it will cost $12 - $20 per quart. So they are a poor value if all you need is cleaning.
What kind of vehicle/ engine/ driving style are we talking about and what symptoms are you experiencing that make you think you need to clean the engine?