The expression started during WWII for equipment patched
together with German equipment. Jerry was American military slang
for Germans.
Answer
The expression "jerry-rig(ged)" is a probable US corruption of a
much older term from the days of sail, "jury rig(ged)" which meant
the same thing, namely fixing something so one can get home, a
makeshift repair, for instance a ship is dismasted, a replacement
mast is rigged from a spare spar, a boom, the remains of the broken
mast, or a smaller mast, depending what is available and what the
crew is able to lift and lash into place.
The term "jerry rig" may also be a blending of "jerry-built"
namely something shoddily or poorly made, and jury rig. The "jerry"
has nothing to do with Germans, and in fact the slang term for
German soldiers "Jerry" dates to WWI and is a British term.