As far as my little German goes, translation for this should be:
Es ist ich.
But here it says:
Is my translation correct?
No. It isn't. The correct translation is
Ich bin es (i.e. Ich bin's)
Das bin ich.
In this sentence, the subject in German is "ich", and not the third person, as in your translation. Note that in German, you don't have to capitalize ich.
I wouldn't try to translate everything from English so literally, for you will see soon how peculiar is the order of the elements in sentence.
Usually, It's me would be translated as Ich bin es when asked Who is it? (like on the phone or at the door), so
c.p.'s answer about says it all.
I'd just like to add another connotation in the slightly varied context of asking Is it just me, or ..., which would be translated as Geht es nur mir so, oder ... or Liegt es an mir, oder ..., and not as Bin es nur ich, oder....
Literally it's me would be Es ist ich. --> It is me. Flipping this around in German goes to: Ich ist es. --> Me is it. But in German the correct form of "sein" related to "ich" is "bin". The result is: Ich bin es. Shortened to: Ich bin's.
You should note that this is a grammatically peculiar construction anyway as you can see from the discussions on whether it should be “it is me” or “it is I” in English. For some reason
Es ist ich.
(how do I mark incorrect grammar?) does not work at all in German. Neither does
Es ist du.
On the other hand
„Wer ist gekommen?“ „Es ist der Weihnachtsmann!“
is correct, and in the same way you could correctly say
Es ist er.
The latter sounds a bit strange, though. I am not quite sure why it is this way. I imagine that although here „es“ is technically the subject, „er“ is the secret subject.