I'm quite sure either you did not copy the message correctly here or your friend made a typo and forgot a "く". Given the context it is most likely: 私に描いてくれない?
This means simply "would you draw it for me?" or maybe "on me" given the context of body paint.
It is using the te-form of the verb plus くれる. This bears the meaning of o do something for me (the asker) or somebody’s sake.
The general construction is:
Giver + は/が + Receiver + に + Verb-てform + くれる/くださる
To be more specific, くれる in your example is in the negative form くれない and it is a colloquial way of the more polite form くれませんか? This is simply a way to ask politely for something using an interrogative negative. In English something like "Wouldn't you (be so kind to) do Verb for me?"
Note that in particular Verb-てform + くれる also conveys a sense of gratitude from the receiver towards the giver (as someone made you the favor of doing Verb).
You can see more about this here and here.