The phrase sounds similar to the following:
I will deliver you unto trouble
I will deliver you into their hands
After swapping out "deliver" for "give", it seems logical that it is an error derived from "unto". This phrasing is common in the Holy Bible:
Matthew 24:9 Then they will deliver you unto tribulation and will kill you, and you will be hated by all the nations on account of my name.
Isiah 65:12 I will deliver you unto the sword.
Typical English usage of "give you into" would suggesting being given into a location or container:
I will give you into their hands
Even something like "give you into jail" doesn't sound right. "Put you into jail" sounds better.