Politely, without being sarcastic or testy, tell your coworker that it is your mug, and you'd like to use it - point out that it is moved by the cleaner, perhaps, and that you intend to store it on your desk to avoid causing problems.

If that seems fussy, well so be it - be fussy, or don't be fussy, but don't be fussy and try to hide it, or make it some unsaid grievance. The essence of this seems to be that you don't like what they're doing but you can't quite bring yourself to acknowledge the pettiness of the behaviour. If you think it is that petty, why do you care so much?

I'm slightly troubled by the existing answers; they are either evasive (silently hoard the cup), passive aggressive (lock mug, writing your name on the mug, add bitterant(!!)) or outright aggressive (take mug from colleague, pour contents down sink). Aggression (passive or active) and evasion are not constructive ways to behave in a contained envinronment like the workplace. If you are passive aggressive, and it happens again, next time you'll be angry, and quite possibly with no one knowing why.