Just one month after the introduction of The Spat Family series, Hal Roach began producing the Will Rogers series. Many of the films exist today (I think there are only 2 missing: High Brow Stuff and Gee Whiz Genevieve), with the majority of them being below average in terms of comedy and/or quality.
An untitled film was supposedly shot from November 6-15, 1923 (production R-8) but not released, according to the Rob Stone/Robert Demoss list.
For a full list of films Will Rogers appeared in for Hal Roach, please see his individual page.

13 Will Rogers

All films Hal Roach/Pathé Exchange and in order of release.
Jus' Passin' Through (Oct 14, 1923)
Hustlin' Hank (Nov 11, 1923)
Uncensored Movies (Dec 9, 1923)

Two Wagons - Both Covered (Jan 6, 1924)
The Cowboy Sheik (Feb 3, 1924)
The Cake Eater (Mar 2, 1924)
Big Moments From Little Pictures (Mar 30, 1924)
High Brow Stuff (Apr 27, 1924)
Going To Congress (May 25, 1924)
Don't Park There (Jun 22, 1924)
Our Congressman (Jul 20, 1924)
A Truthful Liar (Aug 17, 1924)
Gee Whiz, Genevieve (Sep 28, 1924)