So far, the oldest I have found is LZ-127 Graf Zeppelin, first flight in 1928. It used a propeller-driven generator to power its radios and a second one (with buffer battery) to keep the ship illuminated. In the drawing below (source) they are indicated as "Wind-Dynamo", being on both sides of the main gondola.
I am rather sure that the wartime Zeppelins used those generators as well, but have yet to find proof for it.
LZ-127 on August 26, 1929, in Los Angeles (source). The right generator is circled in red.
EDIT: Now I have found a source that attributes a RAT to the Zeppelin Staaken Riesenflugzeuge of WW I. The source is Tom Morrison's book "Quest for All-Weather Flight" and it says on page 28:
In November 1917 the Drexler bank indicator was introduced instead [of the Anschütz gyro]. Much simpler than the Anschütz instrument, it weighed only 5 kg (11 pounds). It was powered by electricity from a generator driven by a small propeller in the slipstream and took less than a minute to run up to speed.
So this dates the first RAT back to November 1917. Sorry, no online sources.
ANOTHER EDIT: I could have thought of that earlier. Really! Igor Sikorsky illuminated the cabin of his Ilya Muromets four-engined giant airplane using light bulbs, powered by a wind-driven generator, too. Wikipedia cites a Sikorsky source from 1938 as:
Lighting was provided by a wind-driven generator and heating was supplied by two long engine exhaust pipes which passed through the corners of the cabin.
Since the earlier S-21 Russky Vityaz had already a similar cabin, it is likely that the first RAT was used as early as 1913. But the first source I found so far firmly establishes it in 1914 if not earlier, in a civilian passenger airplane later used as a bomber. Not an airliner, though, because those came later.
Russky Vityaz. Clearly visible is the electric searchlight in the open fuselage nose stand and less visible (circled in red) the wind-driven generator used to power it. At least that is what I think it is.
Wikipedia says about the legal status of this picture: This work is in the public domain in the United States because it was published (or registered with the U.S. Copyright Office) before January 1, 1926