I found this in The New York Daily News, Nov. 8, 1925, pg. 44. The theater page.

Other news on the page:

• The longest-running Broadway play is “Abie's Irish Rose,” 1,478 performances in, which also makes it the long-running play in Broadway history up to that point. Its record (eventually more than 2,000 performances) will be usurped by “Tocacco Road” in the 1930s, which will be usurped by “Life with Father” in the '40s, which apparently won't be usurped until “Fiddler on the Roof” in the '70s. The Broadway touring show stars George Brent, who will co-star with Cagney in “The Fighting 69th” in 1940.
• Also playing is “Is Zat So?” starring James Gleason and Robert Armstrong. The latter will later star in “King Kong,” and play Cagney's truculent boss in “G-Men.” 
• A 1921 comedy by A.A. Milne, “The Dover Road,” is opening. The following year, Milne will publish a children's book about a bear and his friends that will be a mild hit. 
• Buster Keaton's comedy “Go West” is playing at Loew's State & Metropolitan Theater.
• An actress wearing trousers instead of a short skirt, in Ibsen's “The Master Builder,” gets prominent notice.

Cagney's partner in red-haired thatchery, Charles Bickford, also carved out a successful career in the movies, with more than 100 credits on IMDb, and three Academy Award nominations for supporting actor: “The Song of Bernadette,” “The Farmer's Daughter,” “Johnny Belinda.” I don't think he ever acted with Cagney on screen.

From Cagney By Cagney:

But there was relief the following year, and it came because of my hair. Maxwell Anderson had written a play, Outside Looking in, based on the autobiography of writer-hobo Jim Tully. One of the leading characters was “Little Red,” and because there were virtually only two actors in New York with red hair, Alan Bunce and myself, there wasn’t much competition. I assume I got the part because my hair was redder than Alan’s. The show opened at the Greenwich Village Theatre on Seventh Avenue in September 1925. One of the producers was Eugene O’Neill, and he came backstage one night, looked at me, and said nothing. I suspect that was because he had nothing to say. In any case, the play got fine notices (Charles Bickford played the lead), and from the tiny 299-seat house in the Village we moved uptown to the capacious Thirty-ninth Street Theatre, where I had no trouble projecting my voice because of my ample vaudeville experience. After the first act in the new theatre, Maxwell Anderson came backstage and said, “Gather around, boys, gather around.” We gathered. “Now I want everybody here to speak twice as loud and twice as fast. You hear?” Then, seeing me, he said, “Everybody, that is, except you.”

The play ran awhile and got good notices. In Life magaine, drama critic Robert Benchley wrote: “Wherever Mr. MacGowan found two red-heads like Charles Bickford and James Cagney, who were evidently born to play Oklahoma Red and Little Red, he was guided by the Casting God. Mr. Bickford's characterization is the first most important one of the year ... while Mr. Cagney, in a less spectacular role, makes a ten-minute silence during his mock-trial scene something that many a more established actor might watch with profit.”