I recently rescued two male baby rats from a shelter. They're assumed to be brothers and they have both warmed up to me over the two months or so that I've had them.
While I expect the occasional accident while handling them, one of the rats has made it clear that he is urinating on me on purpose. For instance, if I walk by the cage and I say hi to them, let them kiss my fingers etc, he will sometimes lift his entire body up by climbing up the cage a bit, so that his genitals are near my fingers, and he'll pee. I assume that the purpose is to mark me as his territory, but I don't believe this is a behavior that is healthy to tolerate. I don't want either rat to feel that only they can enjoy my company. I obviously don't like washing my hands because my rat decided to pee on me, either. I haven't noticed my other rat performing this behavior.
Can/should I do something about this?