I have seen both "as God is my witness", which makes sense but sort of puts God in a supportive role, and "as God as my witness", which sounds wrong to me but I don't know, might be an olde tyme phrasing that is only used in that phrase.
The phrase is "As God is my witness ..." I've never heard the other. Here's an emphatic example:
Now that you've posted a link in chat to where you saw the "as" version, I have to tell you that the YouTube title is simply a typo or a mistake. And the actor is clearly saying "As God is my witness I thought turkeys could fly."
The funny thing is, that Gone With the Wind link also is titled "As God as my witness" but Vivien Leigh clearly says "As God is my witness" — several times. YouTube is the Niagara Falls of poor English.
"As God is my witness: [statement]"
... can be rephrased as...
"With God witnessing me say this: [statement]"
"As" is used as a conjunction: "Used to indicate that something happens during the time when something is taking place" -- God is witnessing me as I speak.
"Is" is used, as usual, as the 3rd person singular of "be".
Christian theology says that God is always watching you and witnessing; but by drawing attention to it, the speaker is reminding us that they are thinking about it, and hence are not lying or making idle promises.
"As God as my witness" is a mis-transcription, possibly caused by the actor's accent.
I suppose the first "as" misleads speakers unfamiliar with grammar to think that they need the second one. But this is, clearly, a mistake