In the sense you cite, it’s two words: you are in charge of something because you have the charge (task/responsibility) of doing it.
‘Encharge’ does exist, but it means something else. Apparently, according to the OED, it can be a noun meaning ‘injunction’ (though I’ve never heard of this—it is marked as obsolete, too).
If I see the word ‘encharge’, though, I will normally assume that it is a verb meaning ‘to give [someone] [something] as charge/task/responsibility’:
He was encharged with completing the project and bringing in the contract.
Even in this usage, I would not be very likely to use the word myself, but if I saw it, that is what I would assume it to be.